MCQ Questions for Class 9 Maths Surface Areas And Volumes Quiz 11

Mohit painted the outside of a box of length

$2.5m$ , breadth

$2m$ and height

$1m$ . How much area did he cover, if he painted all except the bottom of the box?

0%
$20m^2$
0%
$16m^2$
0%
$54m^2$
0%
$14m^2$

Explanation

Area Mohit painted

$= 2(2.5\times 2+2\times 1+2.5\times 1)-(2.5\times 2)$

$=2(5+2+2.5)-(5)$

$=2(9.5)-5$

$=19-5$

$=14m^{2}$

1064817_1163972_ans_0c6d15192ead4bb0b30615859ae8ca0d.png

An aquarium is in the form of a cuboid whose external measures are

$80cm\times 30cm\times 40cm$ . The base side faces and back face are to be covered with a coloured paper. Find the area of the paper needed?

0%
$3000cm^2$
0%
$5000cm^2$
0%
$8000cm^2$
0%
$7000cm^2$

Explanation

Area of paper required

$=$ area of base

$+$ 2 area of side

$+$ area of back

$=(80 \times 30) + 2(30 \times 40)+(80 \times 40)$

$=2400+2400+3200$

$=8000cm^{2}$

1064821_1164747_ans_63e20f6936c14c02aaf4333b44071ee7.png

The curved surface area of a cylinder of the base radius

$7\text{ cm}$ and height

$25\text{ cm}$ .

0%
$1100\text{ cm}^3$
0%
$1100\text{ cm}^2$
0%
$1408\text{ cm}^3$
0%
$1408\text{ cm}^2$

Explanation

$\because$ Curved Surface area of cylinder

$=2\pi rh$

Given:

$r=$ radius

$=7\text{ cm}$

$h=$ height

$=25\text{ cm}$

$\therefore$ Curved Surface Area

$=2\times \cfrac{22}{7}\times 7\times 25$

$\text{cm}^{2}$

$=50\times 22$

$\text{cm}^{2}$

$\therefore$ Curved Surface Area of cylinder

$=1100\text{ cm}^{2}$

A water tank is 1.4m long, 1m wide and 0.7m deep, then the volume of the tank in litres

0%
780 Litres
0%
860 Litres
0%
980 Litres
0%
none of these

Explanation

Water tank is

$1.4m$ long,

$1m$ wide and

$0.7m$ deep

Volume of tank

$=1.4\times 1\times 0.7$

$=0.98{ m }^{ 3 }$

$=0.98\times 1000$ litres

$=980$ litres

Answer (C)

Find the total surface area of a hemisphere and a solid hemisphere each of radii

$10\text{ cm}$ (Use

$\pi = 3.14)$ .

0%
$628\ \text{cm}^{2}$ and $942\ \text{cm}^{2}$ respectively
0%
$314\ \text{cm}^{2}$ and $471\ \text{cm}^{2}$ respectively
0%
$1256\ \text{cm}^{2}$ and $1884\ \text{cm}^{2}$ respectively
0%
None of these

Explanation

We have,

$r = 10\ \text{ cm}$

Total surface area of a hemisphere

$=2\pi r^2$

Total surface area of a solid hemisphere

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

$\therefore$ Total surface area of a hemisphere

$=2\times 3.14\times 10\times 10\, \text{cm}^{2}=628\, \text{cm}^{2}$

The total surface area of a solid hemisphere

$=3\pi r^{2}=3\times 3.14\times 10\times 10\, \text{cm}^{2}$

$= 942\, \text{cm}^{2}$

The volume of hollow sphere is

0%
$\frac { 4 }{ 3 } \pi \quad \left( { R }^{ 3 }-{ r }^{ 3 } \right) { cm }^{ 3 }$
0%
$\frac { 2 }{ 3 } \pi \quad \left( { R }^{ 3 }-{ r }^{ 3 } \right) { cm }^{ 3 }$
0%
$\frac { 1 }{ 2 } \pi \quad \left( { R }^{ 3 }-{ r }^{ 3 } \right) { cm }^{ 3 }$
0%
$\frac { 5 }{ 6 } \pi \quad \left( { R }^{ 3 }-{ r }^{ 3 } \right) { cm }^{ 3 }$

Explanation

Where,

$R$ is a radius of a sphere.

To find volume of a hollow sphere, we have to subtract the volume of the inner sphere from the volume of the outer sphere.

Let us assume the radius of outer sphere be

$R$ and the radius of the inner radius be

$r.$

The volume of a outer sphere

$=\dfrac{4}{3}\pi R^3\,cm^3$

The volume of a inner sphere

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

$\therefore$ Volume of hollow sphere

$=$ The volume of a outer sphere

$-$ The volume of a inner sphere

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

$=\dfrac{4}{3}\pi(R^3-r^3)\,cm^3$

1497207_1269483_ans_ab40b1890d7c4bc4aff59bfe32ad06cb.png

A right circular cylinder tunnel of diameter

$2 \text{ m}$ and length

$40 \text{ cm}$ is to be constructed from a sheet of iron. The area of the sheet required in

$\text{ m}^2$ is

0%
$\dfrac{4}{5}\pi$
0%
$80\pi$
0%
$160\pi$
0%
$200\pi$

Explanation

Area of the required iron sheet

$=$ Curved surface area of the cylinder

$\because$ Curved surface area of cylinder

$= 2\pi rh$

$\implies$ Area

$=2\pi\times \dfrac{40}{100}$

$[\because 1\text{ m}=100\text{ cm}$ and

$r=\dfrac{D}{2}=\dfrac{2}{2}=1\text{ m}]$

$\implies$ Area

$=\dfrac{4\pi}{5}\text{ m}^2$

The diameter of the base of a right circular cylinder is

$21\mathrm { cm }$ and its height is

$10\ \mathrm { cm }$ . What is the area of the curved surface?

0%
$660\mathrm { cm } ^ { 2 }$
0%
$930\mathrm { cm } ^ { 2 }$
0%
$1320\mathrm { cm } ^ { 2 }$
0%
$640\mathrm { cm } ^ { 2 }$

Explanation

$Diameter =21\ cm$

$Radius=\dfrac{21}{2}\ cm$

$Height=10\ cm$

We know that the curved surface area of the cylinder

$=2\pi r h$

$=2\times \dfrac{22}{7}\times \dfrac{21}{2}\times 10$

$=220\times 3$

$=660\ cm^2$

The diameter of a cylinder is

$28$ cm and its height is

$20$ cm find the curved surface area.

0%
$1760$ sq.cm
0%
$17600$ sq.cm
0%
$1706$ sq.cm
0%
none of these

Explanation

Diameter of the cylinder

$=28$ cm

$\therefore$ Radius of the cylinder

$=\dfrac{28}{2}$

$=14$ cm

Height of the cylinder

$=20$ cm

$\text{Curved surface area}=2\pi rh\\=2\times \dfrac{22}{7}\times 14\times 20\\=1760\ sq.cm$

The diameter of a cylinder is

$28$ cm and its height is

$20$ cm find the total surface area.

0%
$2992$
0%
$2090$
0%
$2900$
0%
$2099$

Explanation

Diameter of the cylinder

$=28$ cm

$\therefore$ Radius of the cylinder

$=r=\dfrac{28}{2}=14$ cm

Height of the cylinder

$=h=20$ cm

Total surface area

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

$=2\times\dfrac{22}{7}\times 14\times\left(14+20\right)$

$=2992$ sq.cm

The diameter of a sphere whose surface area is

$346.5$

$\mathrm { cm } ^ { 2 }$ is:

0%
$5.25$ $\mathrm { cm }$
0%
$5.75$ $\mathrm { cm }$
0%
$11.5$ $\mathrm { cm }$
0%
$10.5$ $\mathrm { cm }$

Explanation

Let radius of sphere be $r$ cm.

Given, the surface area of a sphere $=346.5\ \text{cm}^2$ .

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

$4\pi r^2 = 346.5 cm^2$

${ { r }^{ 2 } }=\cfrac { 346.5 }{ 4\pi }$

$=\dfrac{346.5\times7}{4\times22}$

$=\dfrac{2425.5}{4\times22}$

$=27.5625$

$\implies$ $r=\sqrt { 27.5625 } =5.25\ \text{cm}$ .

Therefore, option $A$ is correct.

If the surface area of sphere is

$(144\pi)\,{m}^{2}$ , then its volume is

0%
$(288\pi)\,{m}^{3}$
0%
$(188\pi)\,{m}^{3}$
0%
$(300\pi)\,{m}^{3}$
0%
$(316\pi)\,{m}^{3}$

Explanation

Surface area of sphere

$=4\pi r^2$

$\Rightarrow 4\pi r^2=144 \pi$

$\Rightarrow r=\sqrt{\dfrac{144}{4}}=\sqrt{\left(\dfrac{12}{2}\right)^2}=6m$

$\Rightarrow$ Volume

$=\dfrac{4}{3}\pi r^3=\dfrac{4}{3}\times \pi \times 6^3=288\pi m^3.$

Hence, the answer is

$\left( 288\pi\right) m^3.$

$'d'$ is diameter of a sphere, then its volume is-

0%
$\dfrac{2}{3}\pi\ d^{3}$
0%
$\dfrac{1}{6}\pi\ d^{3}$
0%
$\dfrac{4}{3}\pi\ d^{3}$
0%
$\dfrac{1}{24}\pi\ d^{3}$

Explanation

Volume of sphere:

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

$r=\dfrac{d}{2}$

$\therefore V=\dfrac{1}{6}\pi d^3$

If the diameter of the base of a cylinder is

$14$ cm and its height is

$12$ cm then the volume of the cylinder in

$m^3$ is

0%
$10.1848$ $m^3$
0%
$0.001858$ $m^3$
0%
$0.001848$ $m^3$
0%
$18.48$ $m^3$

Explanation

Diameter

$= 14$ cm

Height

$= 12$ cm

radius

$(r) = \dfrac {14}{ 2}= 7$ cm

Volume of the cylinder =

$\pi r^{2}h$

$=\dfrac{22}{7}\times 7\times 7\times 12$

$=1848\ cm^{2}$

$=\dfrac {1848}{100} m^{3}$

$= 18.48\ m^{3}$

Volume of a rectangular box (cuboid) with length

$=2ab,$ breadth

$=3ac$ and height

$=2ac$ is

0%
$12a^2bc^2$
0%
$12a^3bc^2$
0%
$12a^2bc$
0%
$2ab+3ac+2ac$

Explanation

Given

Length

$=2ab$

Breadth

$=3ac$

Height

$=2ac$

Volume of cuboid

$=$ length

$\times$ breadth

$\times$ height

$=2ab\times 3ac\times 2ac$

$=12a^3bc^2$

$\therefore$ Hence the correct answer is

$12a^3bc^2$ .

Find the total surface area of the cuboids of length, breadth and height

$12 \mathrm { cm } , 10 \mathrm { cm } , 5 \mathrm { cm }$ respectively.

0%
$460 \ cm^2$
0%
$490 \ cm^2$
0%
$360 \ cm^2$
0%
$230 \ cm^2$

The largest sphere is carved out of a cube of edge 14 cm. The volume of this sphere is:

0%
1370 $\text{cm}^3$
0%
1800 $\text{cm}^3$
0%
1437 $\text{cm}^3$
0%
1734 $\text{cm}^3$

Explanation

The largest sphere that can be carved out of a cube will have diameter equal to length of the side of the cube.

Diameter

$= 14\, \text{cm}$

$\Rightarrow$ Radius,

$r = 7\ \text{cm}$

Volume of the sphere,

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

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

$= \dfrac{4}{3}\times \dfrac{22}{7}\times 7\times 7 \times 7\ \text{cm}^3$

$= \dfrac{88}{3}\times 49\, \text{cm}^{3}$

$= 1437.33\, \text{cm}^{3}$

Mark the correct alternative of the following.
The number of surfaces of a hollow cylindrical object is?

0%
$1$
0%
$2$
0%
$3$
0%
$4$

The area of the floor of a room is

$15{m}^{2}$ . If its height is

$4m$ , then the volume of the air contained in the room is

0%
$60{dm}^{3}$
0%
$600{dm}^{3}$
0%
$6000{xm}^{3}$
0%
$60000{dm}^{3}$

Explanation

The area of the floor

$(A)=15\,m^2$

Height of the room

$(h)=4\, m$

We have to find the volume of the air in the room

So, capacity of the room to contain air,

$V=A\times h$

$=15\times 4$

$=60\,m^3$

$=60\times (10\,dm)^3$ [

$1m=10\,dm$ ]

$=60\times 1000\,dm^3$

$=60,000\,dm^3$

Volume of the air contained in the room is

$60,000\,dm^3.$

The largest sphere is carved out of a cube of side 10.5 cm. Find the volume of the sphere.

0%
$606.375\,cm^{3}$
0%
$66.3\,cm^{3}$
0%
$60.375\,cm^{3}$
0%
$66.375\,cm^{3}$

Explanation

We have,

Diameter of the largest sphere

$= 10.5 cm\Rightarrow 2r = 10.5 cm \Rightarrow r = 5.25\, cm$

$\therefore$ Volume of the sphere

$= \dfrac{4}{3} \times \dfrac{22}{7} \times \left ( 5.25 \right )^{3} \,cm^{3}$

$= \dfrac{4}{3} \times \dfrac{22}{7} \times \left ( \dfrac{21}{4} \right )^{3} cm^{3} = 4 \times 22 \times \dfrac{21^2}{64} cm^3$

$= \dfrac{11 \times 441}{ 8 } \,cm^3 = 606.375\, cm^3$

If the radius of a sphere is doubled, what is the ratio of the volume of the first sphere to that of the second sphere?

0%
$1:8$
0%
$1:4$
0%
$1:27$
0%
$8:1$

Explanation

Let

$V_1$ and

$V_2$ be the volumes of first and second sphere respectively. Then,

$\dfrac{V_1}{V_2} = \dfrac{\left ( \dfrac 4 3 \right )\pi r^3}{\left (\dfrac 4 3 \right )\pi \left ( 2r \right )^{3}} = \dfrac{1}{8}$

The surface area of a

$10\ cm \times 4\ cm\times 6\ cm$ brick is

0%
$84\ cm^2$
0%
$124\ cm^2$
0%
$164\ cm^2$
0%
$180\ cm^2$

Explanation

We know that the total surface area of cuboid

$=2(lb+bh+hl)$

So, the surface area of the brick

$=2(10\times 6+4\times 6+ 4\times 10)$

$=2(40+30+12)$

$=164$

The area of the cardboard needed to make a box of size

$25\ cm\times 15\ cm\times 8\ cm$ will be

0%
$390\ cm^2$
0%
$1390\ cm^2$
0%
$2780\ cm^2$
0%
$1000\ cm^2$

Explanation

We know that total surface area of cuboid

$=2(lb+bh+hl)$

$=2(25\times15+15\times8+8\times25)$

$=2(375+120+200)$

$=1390\ cm^2$

The actual width of a store room is 280 cm. If the scale chosen to make its drawing is 1:7, then the width of the room in the drawing will be 40 cm.

0%
True
0%
False

Explanation

The given statement is true.

Given, the actual width of the storeroom = 208 cm and scale = 1:7

By using the formula Scale =

$\dfrac{size\ of\ drawing}{actual\ size}$

So, width of the room in the drawing = Actual size x scale =

$280\times \dfrac{1}{7}=40\ cm$

Write True or False and justify your answer in the following:
A solid ball is exactly fitted inside the cubical box of side

$a$ . The volume of the ball is

$\frac{4}{3}\pi a^{3}$

0%
True
0%
False

Explanation

False: Clearly from figure when a ball (spherical) is exactly fitted inside the cubical box then diameter of the ball becomes equal to side of cube so

Diameter $= d = a$

$\Rightarrow$ Radius $=r=\dfrac{a}{2}$

$\therefore$ Volume of spherical ball $=\dfrac{4}{3}\pi r^{3}$

$=\dfrac{4}{3}\pi \left ( \dfrac{a}{2} \right )^{3}=\dfrac{4}{3}\pi \dfrac{a^{3}}{8}=\dfrac{1}{6}\pi a^{3}\neq \dfrac{4}{3}\pi a^{3}$

Hence, the given statement is false.

The surface area of a sphere of radius

$7$ cm is:

0%
$88 cm^2$
0%
$616 cm^2$
0%
$661 cm^2$
0%
$308 cm^2$

Explanation

We know,

Surface area of sphere,

$A= 4 \pi r^2$ , where

$r$ is the radius of sphere.

Here,

$r=7\ cm$

Therefore,

$A=4\times \dfrac{22} 7 \times 7 \times 7=616\ cm^2$ .

Hence, option

$B$ is correct.

Volume of two spheres are in the ratio

$64 : 27$ . The ratio of their surface areas is:

0%
$3:4$
0%
$4:3$
0%
$9:16$
0%
$16:9$

Explanation

$\dfrac{V_{1}}{V_{2}}=\dfrac{64}{27}$ [

$V_{1}, V_{2}$ are the volumes of two spheres]

$\Rightarrow \dfrac{\frac{4}{3}\pi r_{1}^{3}}{\dfrac{4}{3}\pi r_{2}^{3}}=\dfrac{64}{27}$ [

$r_{1}, r_{2}$ are the radii of two spheres]

$\Rightarrow \left ( \dfrac{r_{1}}{r_{2}} \right )^{3}=\left ( \dfrac{4}{3} \right )^{3}$

$\Rightarrow \dfrac{r_{1}}{r_{2}}=\dfrac{4}{3}$
Now, the ratio of their surface areas is given by

$\dfrac{T,S.A_{1}}{T.S.A_{2}}=\dfrac{4\pi r_{1}^{2}}{4\pi r_{2}^{2}}=\left ( \dfrac{r_{1}}{r_{2}} \right )^{2}=\left ( \dfrac{4}{3} \right )^{2}=\dfrac{16}{9}$
Hence, the required ratio

$16 : 9$ verifies the given option.

If the diameter of a sphere is d, then it's volume is

0%
$\frac{1}{3} \pi d^3$
0%
$\frac{1}{24} \pi d^3$
0%
$\frac{4}{3} \pi d^3$
0%
$\frac{1}{6} \pi d^3$

Explanation

If the diameter of a sphere is d, then it's volume is

$\frac{1}{6} \pi d^3$

The ratio of the radii of two spheres is

$4:5$ . Find the ratio of their total surface areas is:

0%
$5 : 4$
0%
$4 : 5$
0%
$16 : 25$
0%
$25 : 16$

Explanation

Given, the ratio of radii of two spheres is

$4:5$ .

We know, the surface area of a sphere

$=4 \pi r^2$ .

Let

$r_1$ and

$r_2$ be the radii of the two sphere,

i.e.

$r_1 : r_2=4:5=\dfrac{4}{5}$ .

Then, the areas of the spheres be

$4 \pi r_1^2$ and

$4 \pi r_2^2$ .

Therefore, the ratio of their surface area

$=\dfrac{4 \pi r_1^2}{4\pi r_2^2}\\=\dfrac{r_1^2}{r_2^2}\\=(\dfrac{r_1}{r_2})^2\\=(\dfrac{4}{5})^2\\=\dfrac{16}{25}\\=16:25$ .

Hence, option

$C$ is correct.

A hollow cylinder has only

0%
curved surface area
0%
total surface area
0%
volume
0%
Perimeter

CBSE Questions for Class 9 Maths Surface Areas And Volumes Quiz 11 - 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 11 - MCQExams.com

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Practice Class 9 Maths Quiz Questions and Answers

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