MCQ Questions for Class 9 Maths Surface Areas And Volumes Quiz 7

The side of the base of a dice is

$5.5$ mm. Find the surface area of a dice whose edges are squares.

0%
$\displaystyle 181.5{ mm }^{ 2 }$
0%
$\displaystyle 90.21{ mm }^{ 2 }$
0%
$\displaystyle 180.2{ mm }^{ 2 }$
0%
$\displaystyle 120.4{ mm }^{ 2 }$

Explanation

Given, side of base

$=5.5$ mm

Total surface area of a cube

$=$

$\displaystyle 6\times$ side

$^{ 2 }$

$\displaystyle =6\times 5.5\times 5.5$

$\displaystyle =181.5{ mm }^{ 2 }$

Find the surface area of a cube with side

$\displaystyle 12$ m

0%
$\displaystyle 814{ m }^{ 2 }$
0%
$\displaystyle 864{ m }^{ 2 }$
0%
$\displaystyle 854{ m }^{ 2 }$
0%
$\displaystyle 841{ m }^{ 2 }$

Explanation

Total surface area of a cube

$=$

$\displaystyle 6\times$ side

$^{ 2 }$

$\displaystyle =6\times 12\times 12$

$\displaystyle =864{ m }^{ 2 }$

A cubical water tank measures

$3$ feet sides. Find its surface area.

0%
$\displaystyle 9{ ft }^{ 2 }$
0%
$\displaystyle 50{ ft }^{ 2 }$
0%
$\displaystyle 52{ ft }^{ 2 }$
0%
$\displaystyle 54{ ft }^{ 2 }$

Explanation

$Surface\ area\ of\ a\ cube=6\times Side^2$

$side=3ft$

$Surface\ Area=6\times 3^2$

$Surface\ Area=6\times 9$

$Surface\ Area=54ft^2$

The length of the side is

$3.9$ ft. Find the surface area of a cube .

0%
$\displaystyle 41.82{ ft }^{ 2 }$
0%
$\displaystyle 94.16{ ft }^{ 2 }$
0%
$\displaystyle 91.26{ ft }^{ 2 }$
0%
$\displaystyle 40.41{ ft }^{ 2 }$

Explanation

Given, length of side

$=.9$ ft

Total surface area of a cube

$=$

$\displaystyle 6\times$ side

$^{ 2 }$

$\displaystyle =6\times 3.9\times 3.9$

$\displaystyle =91.26{ ft }^{ 2 }$

The curved surface of a cylinder is

$\displaystyle 1000{ \ mm }^{ 2 }$ and the radius is

$20$ mm. Find height of the cylinder. (Round off the answer to nearest whole number).

0%
$\displaystyle 8{\ mm }$
0%
$\displaystyle 9{\ mm }$
0%
$\displaystyle 7.9{\ mm }$
0%
$\displaystyle 7.96{\ mm }$

Explanation

Curved surface area of cylinder is

$A=2πrh$

Here, the curved surface area is

$A=1000$ mm

$^2$ the radius is

$r=20$ mm.

Thus,

$A=2πrh\\ \Rightarrow 1000=2\times \frac { 22 }{ 7 } \times 20\times h\\ \Rightarrow 1000\times 7=2\times 22\times 20\times h\\ \Rightarrow 7000=880\times h\\ \Rightarrow h=\frac { 7000 }{ 880 } =7.96$

Hence, height of the cylinder is

$7.96$ mm.

The curved surface area of the cylinder is

$2\pi r h$ where as surface area of the cylinder is

0%
$\pi r(r+h)$
0%
$\pi rl(r+h)$
0%
$2\pi r(r+h)$
0%
$2\pi r^2l(r+h)$

Explanation

The curved surface area of the cylinder is

$2\pi r h$ where as surface area of the cylinder is

$2\pi r(r+h)$ .
Surface area includes curved surface area and two circular bases of the cylinder.

The diameter of a cylinder is

$12$ m and its height is

$10$ m. Find the curved surface area of a cylinder.

0%
$\displaystyle 240\pi { cm }^{ 2 }$
0%
$\displaystyle 120\pi { m }^{ 2 }$
0%
$\displaystyle 220\pi { m }^{ 2 }$
0%
$\displaystyle 230\pi { mm }^{ 2 }$

Explanation

Curved surface area of cylinder is

$A=2πrh$

Here, the diameter is

$12$ m and therefore, the radius is half of diameter that is

$r=6$ m and height is

$10$ m.

Thus,

$A=2πrh=2\times π\times 6\times 10=120π$ m

$^2$

Hence, the curved surface area of the cylinder is

$120π$ m

$^2$ .

Choose the correct formula for surface area of a cylinder.

0%
$\displaystyle 2\pi { r }^{ 2 }+2\pi rh$
0%
$\displaystyle \pi { r }^{ 2 }+\pi rh$
0%
$\displaystyle 2\pi r+2\pi rh$
0%
$\displaystyle 2\pi { r }^{ 2 }+\pi rh$

Explanation

A cylinder comprises two circles and one rectangle as given in the figure

The surface area of a circle is

$\pi r^2$ where

$r$ is the radius and the surface area of a rectangle is

$2\pi rh$ .

$\implies$ Surface area of cylinder

$=2\times$ area of the circular base

$+$ area of the rectangle

$\Rightarrow$ Surface area of cylinder

$=2\pi r^2+2\pi rh$

Find the area of the curved surface of a cylindrical box with radius 12 inches and height 20 inches.

0%
$\displaystyle 1505.1{ in }^{ 2 }$
0%
$\displaystyle 1506.5{ in }^{ 2 }$
0%
$\displaystyle 1507.5{ in }^{ 2 }$
0%
$\displaystyle 1507.2{ in }^{ 2 }$

Explanation

Curved surface area of cylinder is

$A=2πrh$

Here, the radius is

$12$ in and height is

$20$ in.

Thus,

$A=2πrh=2\times 3.14\times 12\times 20=1507.2$ in

$^2$

Hence, the curved surface area of the cylinder is

$1507.2$ in

$^2$ .

Find the surface area of the cylinder shown above:

0%
$\displaystyle 0.46\pi$
0%
$\displaystyle 0.46\pi { m }^{ 3 }$
0%
$\displaystyle 0.46\pi { m }^{ 2 }$
0%
$\displaystyle 0.46\pi cm$

Explanation

Given: Radius of cylinder

$r=0.1m$ and Height

$h=2.2m$ .

Surface area of a cylinder =

$\displaystyle 2\pi r\left( r+h \right)$

$\displaystyle =2\times \pi \times 0.1\left( 0.1+2.2 \right)$

$\displaystyle =2\times \pi \times 0.1\left( 2.3 \right)$

$\displaystyle =0.46\pi { m }^{ 2 }$

So, option C is correct.

Find the surface area of a cylinder:

$r=9\ in, h=18\ in$

0%
$\displaystyle 1526.04{\ in }^{ 2 }$
0%
$\displaystyle 1525.03{\ in }^{ 2 }$
0%
$\displaystyle 1526.04\ in$
0%
$\displaystyle 1526.04{\ in }^{ 3 }$

Explanation

Surface area of cylinder is

$A=2πr(r+h)$

Here, radius is

$r=9$ in and the height is

$h=18$ in.

Thus,

$A=2πr(r+h)=2\times 3.14\times 9(9+18)=56.52\times 27=1526.04$

Hence, the surface area of the cylinder is

$1526.04$ in

$^2$ .

The volume of a cylinder is

$616$ cubic feet and height

$4$ feet. Find its curved surface area. (Use

$\displaystyle \pi ={ 22 }/{ 7 }$ )

0%
$\displaystyle 88{ ft }^{ 2 }$
0%
$\displaystyle 198{ ft }^{ 2 }$
0%
$\displaystyle 79{ ft }^{ 2 }$
0%
$\displaystyle 176{ ft }^{ 2 }$

Explanation

Volume of a cylinder

$=$

$\displaystyle \pi { r }^{ 2 }h$

$\Rightarrow \displaystyle 616=\frac { 22 }{ 7 } \times { r }^{ 2 }\times 4$

$\Rightarrow \displaystyle \frac { 616\times 7 }{ 22\times 4 } ={ r }^{ 2 }$

$\Rightarrow \displaystyle { r }^{ 2 }=49$

$\Rightarrow \displaystyle r=\sqrt { 49 } =7ft$

Curved surface area

$=$

$\displaystyle 2\pi rh$

$\displaystyle =2\times \frac { 22 }{ 7 } \times 7\times 4$

$\displaystyle =176$ square feet

The inner radius of a cylindrical wooden furniture is

$8$ m and its outer radius is

$12$ m. The height of the furniture is

$35$ m. Find its lateral surface area. (Use

$\displaystyle \pi ={ 22 }/{ 7 }$ ).

0%
$\displaystyle 880{ \ m }^{ 3 }$
0%
$\displaystyle 880{\ m }^{ 2 }$
0%
$\displaystyle 88{ \ m }^{ 2 }$
0%
$\displaystyle 880{\ mm }^{ 2 }$

Explanation

Given: Inner radius of the cylindrical furniture (r)

$=8$ m

Outer radius of the cylindrical furniture (R)

$=12$ m

Height of the furniture (h)

$=35$ m

$\therefore$ Lateral Surface area

$=2\pi(R-r)h$

$=2\times \dfrac{22}{7}\times (12-8)\times 35$

$=2\times 22\times 4 \times 5$

$=880 m^2$

If the lateral surface of a cylinder is

$\displaystyle 500\ { cm }^{ 2 }$ and ts height is

$10\ cm$ , then find radius of its base. (use

$\displaystyle \pi =3.14$ ).

0%
$6.92\ cm$
0%
$7.96\ cm$
0%
$\displaystyle 6.54\ cm$
0%
$\displaystyle 8.22\ cm$

Explanation

Here, the lateral surface area is

$A=500\ cm^2$ and the height is

$h=10\ cm$

Let, the radius be

$r$

Lateral surface area of cylinder is

$A=2πrh$

Thus,

$A=2πrh\\ \Rightarrow 500=2\times 3.14\times r\times 10\\ \Rightarrow 500=62.8r\\ \Rightarrow r=\dfrac { 500 }{ 62.8 } =7.96$

Hence, radius of the cylinder is

$7.96\ cm$ .

The circumference of a circle is

$200$ feet and height is

$12$ feet. Find its curved surface area of a cylinder.

0%
$\displaystyle 2400{ ft }^{ 2 }$
0%
$\displaystyle 2100{ ft }^{ 2 }$
0%
$\displaystyle 2300{ ft }^{ 2 }$
0%
$\displaystyle 2010{ ft }^{ 2 }$

Explanation

Circumference of cylinder is

$C=2πr$

It is given that the circumference is

$200$ feet, therefore,

$C=2πr\\ \Rightarrow 200=2πr\\ \Rightarrow r=\dfrac { 200 }{ 2π } =\dfrac { 100 }{ π }$

Now, curved surface area of cylinder is

$A=2πrh$

Here, the radius is

$\dfrac { 100 }{ π }$ ft and height is

$12$ ft.

Thus,

$A=2πrh=2π\times \dfrac { 100 }{ π } \times 12=2\times 100\times 12=2400$ ft

$^2$

Hence, the curved surface area of the cylinder is

$2400$ ft

$^2$ .

David built a recycling cylindrical bin that is 12 feet long and its base is 56 feet radius. Find the surface area of the bin.

0%
$\displaystyle 23936{\ ft }^{ 3 }$
0%
$\displaystyle 23936{\ ft }^{ 2 }$
0%
$\displaystyle 23950{ \ ft }^{ 2 }$
0%
$\displaystyle 23936\ ft$

Explanation

Surface area of cylinder is

$A=2πr(r+h)$

Here the cylindrical bin has radius

$r=56$ ft and height

$h=12$ ft.

Thus,

$A=2πr(r+h)=2\times 3.14\times 56(56+12)=351.68\times 68=23936.24$

Hence, the surface area of the cylindrical bin is approximately equal to

$23936$ ft

$^2$ .

Find the curved surface area of the cylinder given above:

0%
$\displaystyle 1507.2{ m }^{ 2 }$
0%
$\displaystyle 1527.6{ m }^{ 2 }$
0%
$\displaystyle 1517.8{ m }^{ 2 }$
0%
$\displaystyle 1588.1{ m }^{ 3 }$

Explanation

Given,

Height

$h=40\ m$
Diameter =

$\displaystyle 12m$

Radius

$r= \dfrac {Diameter}{2} = \dfrac {12}{2}\ m = 6$ m

Curved surface area

$=\displaystyle 2\pi rh$

$\displaystyle =2\times 3.14\times 6\times 40\ m^2$

$\displaystyle = 1507.2{ m }^{ 2 }$

So, option A is correct.

The radius of the base of a cylinder is 20 cm and the height is 12 cm. Find the surface area of the cylinder. (Assume

$\displaystyle \pi =3.14$ ).

0%
$\displaystyle 4019.2{ cm }^{ 3 }$
0%
$\displaystyle 4019.2cm$
0%
$\displaystyle 4019.2{ cm }^{ 2 }$
0%
$\displaystyle 4018.6{ cm }^{ 2 }$

Explanation

Surface area of cylinder is

$A=2πr(r+h)$

Here, radius is

$r=20$ cm and the height is

$h=12$ cm.

Thus,

$A=2πr(r+h)=2\times 3.14\times 20(20+12)=125.6\times 32=4019.2$

Hence, the surface area of the cylinder is

$4019.2$ cm

$^2$ .

Find the height of a cylinder that has a diameter of

$10$ feet and a surface area of

$\displaystyle 220{\ ft }^{ 2 }$ . Round your answer to the nearest whole number.
(use

$\displaystyle \pi ={ 22 }/{ 7 }$ ).

0%
$0.1$ ft
0%
$3$ ft
0%
$2$ ft
0%
$1$ ft

Explanation

Surface area of cylinder is

$A=2πr(r+h)$

Here the cylinder has surface area

$A=220$ ft

$^2$ and diameter

$10$ ft and therefore, the radius is half of the diameter that is

$r=5$ ft.

Thus,

$A=2πr(r+h)\\ \Rightarrow 220=2\times \frac { 22 }{ 7 } \times 5(5+h)\\ \Rightarrow 220=\frac { 44 }{ 7 } (25+5h)\\ \Rightarrow 220\times 7=1100+220h\\ \Rightarrow 1540-1100=220h\\ \Rightarrow 220h=440\\ \Rightarrow h=\frac { 440 }{ 220 } =2$

Hence, the height of the cylinder is

$2$ ft.

A cylindrical drum has its height 20 inches and curved surface area as

$\displaystyle 200{ in }^{ 2 }$ . Find surface area of cylindrical drum.(

$\displaystyle \pi ={ 22 }/{ 7 }$ )

0%
$\displaystyle 203.5{ in }^{ 2 }$
0%
$\displaystyle 207.3{ in }^{ 2 }$
0%
$\displaystyle 215.7{ in }^{ 2 }$
0%
$\displaystyle 218.13$

Judah wants to make a cylindrical drum that will fit a bass with a height

$15$ in. and a diameter of

$48$ in. What is the surface area of the drum?

Take

$\pi = 3.14$

0%
$\displaystyle 5810.10in$
0%
$\displaystyle 5810.10{ in }^{ 2 }$
0%
$\displaystyle 5878.08{ in }^{ 2 }$
0%
$\displaystyle 5878{ in }^{ 2 }$

Explanation

Surface area of cylinder is

$A=2πr(r+h)$

Here, diameter is

$48$ in and therefore, the radius is half of diameter that is

$r=24$ in and the height is

$h=15$ in.

Thus,

$A=2πr(r+h)=2\times 3.14\times 24(24+15)=150.72\times 39=5878.08$

Hence, the surface area of the cylindrical drum is

$5878.08$ in

$^2$ .

Edward bought a container of ceralac in the shape of cylinder. If the container has a radius

$10 m$ and a surface area is

$\displaystyle 340\pi$ . What is its height?

0%
$5 m$
0%
$6m$
0%
$7m$
0%
$8m$

Explanation

Surface area of cylinder is

$A=2πr(r+h)$

Here the cylindrical container has surface area

$A=340π$ m

$^2$ and radius

$r=10$ m.

Thus,

$A=2πr(r+h)\\ \Rightarrow 340π=2π\times 10(10+h)\\ \Rightarrow 340π=20π(10+h)\\ \Rightarrow 340π=200π+20πh\\ \Rightarrow 20πh=340π-200π\\ \Rightarrow 20πh=140π\\ \Rightarrow h=\dfrac { 140π }{ 20π } =7$

Hence, the height of the cylindrical container is

$7m$ .

Find the total surface area of the cylinder. (Use

$\displaystyle \pi =3.14$ ).

0%
$\displaystyle 678.99{ ft }^{ 2 }$
0%
$\displaystyle 3881.05{ ft }^{ 2 }$
0%
$\displaystyle 3881.04ft$
0%
$\displaystyle 678.24{ ft }^{ 2 }$

Explanation

Given:

$r=6ft$ and

$h=12ft$

The total surface area of a cylinder =

$\displaystyle 2\pi r\left( r+h \right)$

$\displaystyle =2\times 3.14\times 6\left( 6+12 \right)$

$\displaystyle =2\times 3.14\times 6\left( 18 \right)$

$=\displaystyle 678.24{ ft }^{ 2 }$

So, option D is correct.

The surface area of a cylindrical box is

$\displaystyle 132\ { mm }^{ 2 }$ and its height is

$4 \ mm.$ Find its radius.

0%
$\displaystyle 2$ ${ mm }$
0%
$\displaystyle 3$ ${ mm }$
0%
$\displaystyle 4$ ${ mm }$
0%
$\displaystyle 5$ ${ mm }$

Explanation

Given: Cylindrical box has surface area

$A=132$

$mm^2$ and height

$h=4\ mm$

We know surface area of cylinder is

$A=2πr(r+h)$

Thus,

$132=2\times \dfrac { 22 }{ 7 } \times r(r+4)$

$\Rightarrow 132=\dfrac { 44 }{ 7 } r(r+4)$

$\Rightarrow 132\times 7=44r(r+4)$

$\Rightarrow 924=44r^{ 2 }+176r$

$\Rightarrow 44r^{ 2 }+176r-924=0$

$\Rightarrow r^{ 2 }+4r-21=0$

$\Rightarrow r^{ 2 }+7r-3r-21=0$

$\Rightarrow r(r+7)-3(r+7)=0$

$\Rightarrow r+7=0,\quad r-3=0$

$\Rightarrow r=-7,\quad r=3$

Hence, the radius of the cylindrical box is

$3$ mm.

A skating board rocks back and forth on a wooden cylinder. The cylinder has a radius of 6 inches and a surface area is

$\displaystyle 590{ in }^{ 2 }$ . Find the height of the cylinder. (

$\displaystyle \pi =3.14$ ).

0%
$10$ in
0%
$9.65$ in
0%
$9$ in
0%
$9.5$ in

Explanation

Surface area of cylinder is

$A=2πr(r+h)$

Here the wooden cylinder has surface area

$A=590$ in

$^2$ and radius

$r=6$ mm.

Thus,

$A=2πr(r+h)\\ \Rightarrow 590=2\times \dfrac { 22 }{ 7 } \times 6(6+h)\\ \Rightarrow 590=\dfrac { 44 }{ 7 } (36+6h)\\ \Rightarrow 590\times 7=1584+264h\\ \Rightarrow 4130-1584=264h\\ \Rightarrow 264h=2546\\ \Rightarrow h=\dfrac { 2546 }{ 264 } =9.643$

Hence, the height of the wooden cylinder is

$9.65$ in.

Find the volume of the hemisphere with radius

$6$ cm.

0%
$352.16$ $cm^3$
0%
$452.16$ $cm^3$
0%
$252.16$ $cm^3$
0%
$152.16$ $cm^3$

Explanation

Given, radius of hemisphere

$=6$ cm

Volume of the hemisphere

$=$

$\dfrac{2}{3}\pi r^3$

$=$

$\dfrac{2}{3}\times 3.14 \times 6^3$

$= 452.16$

$cm^3$

A gas cylinder has a diameter of

$14$ m and height is

$0.2$ m. Find its surface area. (

$\displaystyle \pi ={ 22 }/{ 7 }$ )

0%
$\displaystyle 316.512{ mm }^{ 2 }$
0%
$\displaystyle 316.512m$
0%
$\displaystyle 316.512{ m }^{ 3 }$
0%
$\displaystyle 316.512{ m }^{ 2 }$

Explanation

Surface area of cylinder is

$A=2πr(r+h)$

Here the gas cylinder has diameter

$14$ m and therefore, the radius is half of diameter that is

$r=7$ m and height

$h=0.2$ m.

Thus,

$A=2πr(r+h)=2 \times \dfrac {22}{7}\times 7(7+0.2)=316.512$

Hence, the surface area of the gas cylinder is

$316.512m^2$ .

The curved surface area of a cylinder is

$\displaystyle 188.4\ { m }^{ 2 }$ . The height is

$12\ m$ . What is the radius? (use

$\displaystyle \pi =3.14$ ).

0%
$\displaystyle 2\ { cm }$
0%
$\displaystyle 2.5\ cm$
0%
$\displaystyle 2\ m$
0%
$\displaystyle 2.5\ m$

Explanation

Curved surface area of cylinder is

$A=2πrh$

Here, the curved surface area is

$A=188.4\ m^2$ the height is

$h=12\ m$ .

Thus,

$A=2πrh\\ \Rightarrow 188.4=2\times 3.14\times r\times 12\\ \Rightarrow 188.4=75.36r\\ \Rightarrow r=\dfrac { 188.4 }{ 75.36 } =2.5$

Hence, radius of the cylinder is

$2.5\ m$

Find the volume of a sphere whose diameter is

$7.2\ mm$ .

0%
$\displaystyle 195.33{ \ m }^{ 3 }$
0%
$\displaystyle 175.33{ \ mm }^{ 3 }$
0%
$\displaystyle 195.33{ \ mm }^{ 3 }$
0%
$\displaystyle 185.33{\ mm }^{ 3 }$

Explanation

Formula:

Volume of sphere

$=\dfrac{4}{3} \pi r^3$

$r=radius$

Given:

$diameter(d)=7.2\ mm$

$radius(r)=\dfrac{d}{2}=\dfrac{7.2}{2}=3.6\ mm$

$\Rightarrow \dfrac{4}{3} \pi r^3=\dfrac{4}{3}\times 3.14\times (3.6)^3$

$=\dfrac{4}{3}\times 3.6\times 3.6\times 3.6\times 3.14$

$=\dfrac{4}{3}\times 46.656times 3.14$

$=\dfrac{585.999}{3}$

$=195.33\ mm^3$

What is the volume of a sphere? (use

$\displaystyle \pi =3.14$ )

0%
$\displaystyle 6,878.82{\ in }^{ 3 }$
0%
$\displaystyle 6,578.82{ \ in }^{ 3 }$
0%
$\displaystyle 5,878.82{\ in }^{ 3 }$
0%
$\displaystyle 6,808.82{\ in }^{ 3 }$

Explanation

Formula:

Volume of sphere

$=\dfrac{4}{3}\pi r^3$

where,

$r=radius$

Given:

$r=11.8$

After substituting the values in the formula we

$\dfrac{4}{3}\pi r^3 =\dfrac{4}{3}\times 3.14\times 11.8^3$

$=\dfrac{4}{3}\times3.14\times11.8\times11.8\times11.8$

$=\dfrac{20636.481}{3}$

$=6878.82\ in^3$

CBSE Questions for Class 9 Maths Surface Areas And Volumes Quiz 7 - MCQExams.com

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Practice Class 9 Maths Quiz Questions and Answers

CBSE Questions for Class 9 Maths Surface Areas And Volumes Quiz 7 - MCQExams.com

0:0:2

Practice Class 9 Maths Quiz Questions and Answers

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