MCQ Questions for Class 9 Maths Surface Areas And Volumes Quiz 2

Volume of a suitcase with clothes in it is ................... the volume of empty suitcase. (Both suitcases are of same size)

0%
more than
0%
less than
0%
equal to
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none of these

A toy box can fit

$36$ equal sized unit blocks in it. Then its volume is

0%
$36\,sq\,units$
0%
$63\,sq\,units$
0%
$36\,cu\,units$
0%
$62\,cu\,units$

Explanation

$\Rightarrow$ Length of any edge of toy box

$(l)=1\,unit$

$\Rightarrow$ Volume of

$1$ toy box

$=(l)^3$

$=1\,cu\,units$

$\Rightarrow$ Volume of

$36$ equal sized toy box

$=36\times 1\,cu\,units$

$=36\,cu\,units$ .

Fill in the blanks:
Surface area of a cylinder = ............. x ........... + .......... .

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2 $\times$ area of rectangle $+$ area of circle
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2 $\times$ area of circle $+$ area of rectangle
0%
2 $\times$ area of square $+$ area of rectangle
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2 $\times$ area of rectangle $+$ area of rectangle

Explanation

Cylinder is made up of

$2$ circles and one rectangle as shown in the figure.

Length of the rectangle is the circumference of circle. Breadth will be height of cylinder.

Hence cylinder is the addition of two areas of circle and one rectangle.

So, option (b) is correct.

Fill in the blanks :
Curved surface area of a cylinder = ____

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Circumference of a base $\times$ height
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Area of a circle $\times$ radius
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Circumference of a base $\times$ radius
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Area of a circle $\times$ height

Explanation

The curved surface area of a cylinder is the circumference of a base

$\times$ height.

Volume of a cuboid with

$l = 10 cm, b = 12 cm, h = 8 cm$ is

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$96$ cubic cm
0%
$9.6$ cubic cm
0%
$9600$ cubic cm
0%
$960$ cubic cm

Explanation

$\Rightarrow$

$l=10\,cm,\,b=12\,cm$ and

$h=8\,cm$ [ Given ]

$\Rightarrow$ Volume of a cuboid

$=l\times b\times h$

$=10cm\times 12cm\times 8cm$

$=960\,cm^3$

1368172_407729_ans_149f954eab6a4be7bfe6f30f29e0e612.jpeg

Which formula is used to calculate the curved surface area of a cylinder?

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

Explanation

Curved surface area of a cylinder is circumference of a base

$\times$ $ height.
Curved surface area of a cylinder

$=$

$\displaystyle 2\pi rh$ .

Volume of a sphere is calculated by:

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$\displaystyle \frac { 1 }{ 3 } \pi { r }^{ 3 }$
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$\displaystyle \frac { 4 }{ 3 } \pi { r }^{ 2 }$
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$\displaystyle \frac { 4 }{ 3 } \pi { r }^{ 3 }$
0%
$\displaystyle \frac { 2 }{ 3 } \pi { r }^{ 3 }$

Explanation

Volume of a sphere

$\displaystyle =\frac { 4 }{ 3 } \pi { r }^{ 3 }$

Volume of a hemi-sphere

$\displaystyle =\frac { 2 }{ 3 } \pi { r }^{ 3 }$

Where,

$r$ is the radius.

What is the total surface area of a cuboid ?

0%
$2(lb + bh + hl)$
0%
$(l \times b \times h)$
0%
$(l \times b)$
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None of these

Explanation

Let the length, breadth and height of the cuboid be

$l,\ b$ and

$h$ respectively.

The total surface area of a cuboid (TSA) is equal to the sum of the areas of its 6 rectangular faces.

TSA of cuboid

$=l\times b+b\times h+h\times l+l\times b+b\times h+h\times l$

$=2(lb + bh + hl)$

1092940_405281_ans_c26900090cc041ce9e1fdfb3593ae9d4.jpg

Find the volume of a sphere, whose diameter is

$8\ mm$ .(Take

$\pi=3.14$ ) (Round your answer to the nearest tenth).

0%
$\displaystyle 243.6{ mm }^{ 3 }$
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$267.94\ mm^3$
0%
$\displaystyle 1,143.6{ mm }^{ 3 }$
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$\displaystyle 2,143.6mm$

Explanation

Formula:

Volume of sphere

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

where,

$r=radius$

Given:

$r=4mm$

After substituting the values in the formula we get:

$\dfrac{4}{3}\pi r^3=\dfrac{4}{3}\times3.14\times4^3$

$=\dfrac{4}{3}\times3.14\times4\times4\times4$

$=\dfrac{803.84}{3}$

$=267.94\ mm^3$

Calculate the volume of a sphere with radius

$2\ m. (\pi = 3.142)$

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$33.51\ m^3$
0%
$73.51\ m^3$
0%
$63.51\ m^3$
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None of these

Explanation

Vol. of sphere

$V = \dfrac{4}{3}\pi r^{3} = \dfrac{4}{3}\times 3.14 \times 2^{3}$

$V =\dfrac{4}{3}\times 3.14 \times 8$

$=\dfrac{32}{3}\times 3.14$

$=\dfrac{100.48}{3}=33.49\ m^3$

Find the volume of a sphere of radius given below:

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$\displaystyle 1,706.25{ \ ft }^{ 3 }$
0%
$\displaystyle 1,766.15{\ ft }^{ 3 }$
0%
$\displaystyle 1,866.25{\ ft }^{ 3 }$
0%
$\displaystyle 1,766.25{\ ft }^{ 3 }$

Explanation

Using formula volume of sphere =

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

$r=radius$

Given:

$radius(r)=7.5\ ft$

$\Rightarrow \dfrac{4}{3} \pi r^3=\dfrac{4}{3}\times 3.14 \times 7.5^3$

$=\dfrac{4}{3} \times 7.5 \times 7.5 \times 7.5 \times 3.14$

$=\dfrac{4}{3} \times 421.875 \times 3.14$

$=\dfrac{5298.75}{3}$

$=1766.25\ ft^3$

The surface area of a sphere is given by the formula:

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$\displaystyle 4\pi { r }^{ 2 }$
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$\displaystyle 4\pi r$
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$\displaystyle 2\pi { r }^{ 2 }$
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$\displaystyle \dfrac {1}{2}\pi { r }^{ 2 }$

Explanation

We know that the surface area of a sphere is exactly four times the area of a circle with the same radius.

Also, area of circle

$=\pi r^2$ .

Then, area of sphere

$=4\times \pi r^2$ .
Therefore, the surface area of a sphere is given by the formula

$\displaystyle 4\pi { r }^{ 2 }$ .

Hence, option

$A$ is correct.

Volume of sphere is

0%
$\dfrac{1}{3}\pi r^3$
0%
$\dfrac{4}{3}\pi r^3$
0%
$\dfrac{2}{3}\pi r^3$
0%
$\dfrac{4}{3}\pi r^2$

Explanation

${\textbf{Step -1: Write the formula for volume of sphere}}{\textbf{.}}$

${\text{To find the volume of sphere we have the formula }}\dfrac{4}{3}\pi {r^3}.$

$\text{Where r is the radius of the sphere}$

$\textbf{Hence, option B is the correct answer}$

Calculate the surface area of a sphere of radius

$2.8$ cm.

0%
$98.56$ cm $^2$
0%
$68.56$ cm $^2$
0%
$38.56$ cm $^2$
0%
None of these

Explanation

Given, radius $r=2.8$ cm.

We know that, the surface area of a sphere of radius $r$ $= 4\pi { r }^{ 2 }$

$= 4 \times \dfrac {22}{7} \times 2.8 \times 2.8$

$= 98.56 {cm}^{2}$ .

Therefore, option

$A$ is correct.

The surface area of a cube of side

$27\ \text{cm}$ is

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$2916\ \text{cm}^{2}$
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$729\ \text{cm}^{2}$
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$4374\ \text{cm}^{2}$
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$19683\ \text{cm}^{2}$

Explanation

Let, the given side of square

$=a=27\ \text{cm}$

Surface area of cube

$=6a^2$

$=6(27)^2\ \text{cm}^2$

$=4374\ \text{cm}^2$

Calculate the surface area of sphere.

0%
$\displaystyle 5,024\ cm$
0%
$\displaystyle 314{\ cm }^{ 2 }$
0%
$\displaystyle 5,024{\ m }^{ 2 }$
0%
$\displaystyle 5,024{ \ mm }^{ 2 }$

Explanation

We know, surface area of sphere,

$A=4\pi r^2$ .

Given, diameter,

$d=10\ cm$ .

Then, radius,

$r=\dfrac{d}{2}=\dfrac{10}{2}=5\ cm$ .

After substituting the values in the formula we get:

Surface area of the sphere,

$A=4\times3.14\times5^2$

$=4\times3.14\times5\times5$

$=314\ cm^2$ .

Therefore, option

$B$ is correct.

A ball in the shape of a sphere has a surface area of

$221.76$ cm

$^2$ . Calculate its diameter.

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$8.4cm$
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$7.4cm$
0%
$9.4cm$
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None of these

Explanation

Let radius of sphere be $r$ cm.

We know, surface area of sphere $=4\pi { r }^{ 2 }$

$\implies$ $221.76 cm^2 =4\pi { r }^{ 2 }$

$\implies$ ${ { r }^{ 2 } }=\cfrac { 221.76 }{ 4\pi } =\dfrac{221.76\times 7}{4\times 22}=17.64$

$\implies$ $r=\sqrt { 17.64 } =4.2 cm$ .

Then, diameter of the sphere, $d=2r=2\times4.2=8.4 cm$ .

Therefore, option $A$ is correct.

Which part in the cylinder is included for total surface area?

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curved surface area
0%
curved surface area and two circular bases
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one circular bases
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two circular bases

Find the volumes of rectangular boxes with length, breadth and height in the following table

S.No	Length	Breadth	Height	Volume $(v)=l\times b\times h$
1	$3x$	$4{x}^{2}$	$5$	$v=3x\times 4{x}^{2}\times 5=60{x}^{3}$
2	$3{a}^{2}$	$4$	$5c$	$v=......................$
3	$3m$	$4n$	$2{m}^{2}$	$v=......................$
4	$6kl$	$3{l}^{2}$	$2{k}^{2}$	$v=......................$
5	$3pr$	$2qr$	$4pq$	$v=.....................$

0%

2. $60{a}^{2}c$
0%
5. $24{p}^{2}{q}^{2}{r}^{2}$
0%
4. $36{k}^{3}{l}^{3}$
0%
3. $24{m}^{3}n$

Explanation

Given formula is,

$v=l\times b\times h$

(2) Given,

$l=3a^2,\ b=4,\ h=5c$

$\therefore v=l\times b\times h\\=3a^2\times 4\times 5c\\ =60a^2c$

(3) Given,

$l=3m,\ b=4n,\ h=2m^2$

$\therefore v=l\times b\times h\\=3m\times 4n\times 2n^2\\ =24m^3n$

(4) Given,

$l=6kl,\ b=3l^2,\ h=2k^2$

$\therefore v=l\times b\times h\\=6kl\times 3l^2\times 2k^2\\ =36k^3l^3$

(2) Given,

$l=3pr,\ b=2qr,\ h=4pq$

$\therefore v=l\times b\times h\\=3pr\times 2qr\times 4pq\\ =24p^2q^2r^2$

Find the radius of a solid sphere that has a volume of

$10$ m

$^3$ .

0%
$1.336 m$
0%
$3.336 m$
0%
$2.336 m$
0%
None of these

Explanation

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

$\Rightarrow r = 3 \sqrt{\dfrac{3V}{4\pi }} = \left ( \dfrac{3\times 10}{4\pi} \right )^{1/3}$

$\Rightarrow \boxed{r = 1.336\,m}$

1110220_520264_ans_0a473101b59545c7bf60e2072402ace3.jpg

Calculate the volume of a hemisphere with radius

$7$ cm.

$\left ( \pi = \dfrac{22}{7} \right)$

0%
$718.67$ cm $^3$
0%
$78.67$ cm $^3$
0%
$18.67$ cm $^3$
0%
None of these

Explanation

Formula for volume of hemisphere

$= \dfrac{2}{3}\pi r^{3}$
Given,

$r=7\ cm$
Volume:

$V = \dfrac{2}{3}\times \dfrac{22}{7}\times 7^{3} \\ = \boxed {718.67\ cm^3} \$

Find the radius of a hemisphere with the volume of

$20$ cm

$^3$ .

$(\pi = 3.142)$

0%
$2.121 \text{ cm}$
0%
$4.121 \text{ cm}$
0%
$5.121 \text{ cm}$
0%
None of these

Explanation

Volume of hemisphere is

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

$\Rightarrow r = \left(\dfrac{3V}{2\pi }\right)^{\dfrac{1}{3}}$

$\Rightarrow r = \left ( \dfrac{3\times 20}{2\pi} \right )^{\dfrac{1}{3}}$

$\Rightarrow r = 2.121\,\text{ cm}$

Find the volume of the sphere whose radius is

$5\sqrt 3$ cm.

0%
$2127.72$ cm $^3$
0%
$2720.72$ cm $^3$
0%
$2721.71$ cm $^3$
0%
$2727.27$ cm $^3$

Explanation

$V = \dfrac{4}{3}\pi r^{3} = \dfrac{4}{3}\pi (5\sqrt{3})^{3} = \boxed{2720.7\,cm^{3}}$
1110837_520703_ans_5f9a5c42df63489babc9b6820c521993.jpg

The radius of a spherical balloon increases from

$7$ cm to

$14$ cm as air is being pumped into it. Find ratio of surface areas of the balloon in the two cases.

0%
$\dfrac{3}{4}$
0%
$\dfrac{1}{4}$
0%
$\dfrac{1}{5}$
0%
None of these

Explanation

We know, the surface area of a sphere is

$4\pi r^{2}$ , where

$r$ is the radius.

Let

$r_1$ be the original radius and

$r_2$ be the new radius.

Then,

$r_1=7$ and

$r_2=14$ .

Therefore, the ratio of the surface area will be:

$=\dfrac { 4\pi { r }_{ 1 }^{ 2 } }{ 4\pi { r }_{ 2 }^{ 2 } } =\dfrac { { r }_{ 1 }^{ 2 } }{ { r }_{ 2 }^{ 2 } } =\dfrac { { 7 }_{ }^{ 2 } }{ { 14 }_{ }^{ 2 } } =\dfrac { 1 }{ 4 }$

Hence, the required ratio is

$\dfrac{1}{4}$ .

Therefore, option

$B$ is correct.

The volume of sphere with radius

$3cm$ is .................

${cm}^{3}$ .

0%
$14\pi$
0%
$18\pi$
0%
$2\pi$
0%
$36\pi$

Explanation

Given : Radius

$(r)=3\ cm$

We know, Volume of a sphere

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

$\implies V=\cfrac { 4 }{ 3 } \times \pi \times 3\times 3\times 3$

$\implies V=4\times \pi \times 3\times 3=36\pi$

Hence, volume of a sphere is

$36\pi$ .

If all three parameters of a cuboid are in meters

$(m)$ , then unit of volume of a cuboid is:

0%
$m$
0%
$m^{2}$
0%
$m^{3}$
0%
$cm^{3}$

Explanation

As the volume of a cube is

$length\times length \times length$

If lengths of all are measured in meters.

Then the volume will be measured in

$m^3$ .

Hence, the answer is

$m^{3}$ .

The formula of lateral surface area of cylinder is ________.

0%
$A = 2\pi r h$
0%
$A = 2\pi r$
0%
$A = \pi r^{2}$
0%
$A = 2\pi r^{2}h$

Explanation

Lateral surface area and cylinder

$2\pi rh$

$\therefore$ Part (A) is correct answer.

The surface area of a solid hemisphere is

0%
$\pi { r }^{ 2 }$
0%
$4\pi { r }^{ 2 }$
0%
$\dfrac { 4 }{ 3 } \pi { r }^{ 2 }$
0%
$3\pi { r }^{ 2 }$

Explanation

Surface area of a circle

$=\pi r^2$

Since, the hemisphere is solid, then it will include the base too.

$\therefore$ surface area of a solid hemisphere

$=\pi r^2+2\pi r^2=3\pi r^2$

Hence, option D is correct.

The amount of three-dimensional space occupied by an object is called?

0%
Area
0%
Pressure
0%
Volume
0%
Mass

Find the surface area of a

$10cm \times 4cm \times 3cm$ brick:

0%
84 sq. cm
0%
124 sq.cm
0%
164 sq.cm
0%
180 sq.cm

Explanation

The formula for calculating the surface area of a cuboid of dimensions :

$l \times b \times h$ is :

$2\times (l\times b+b\times h+h\times l)$

Substituting,

$l=10cm$

$b=4cm$

$h=3cm$

Surface area = $2\times (10\times 4+4\times 3+3\times 10)$

$= 2\times (40 + 12 + 30)$

$= 2\times 82 { cm }^{ 2 }$

$= 164 { cm }^{ 2 }$

Hence, the answer is option (C)

CBSE Questions for Class 9 Maths Surface Areas And Volumes Quiz 2 - 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 2 - MCQExams.com

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Practice Class 9 Maths Quiz Questions and Answers

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