## RD Sharma Class 9 Solutions Chapter 18 Surface Areas and Volume of a Cuboid and Cube MCQS

These Solutions are part of RD Sharma Class 9 Solutions. Here we have given RD Sharma Class 9 Solutions Chapter 18 Surface Areas and Volume of a Cuboid and Cube MCQS

Other Exercises

- RD Sharma Class 9 Solutions Chapter 18 Surface Areas and Volume of a Cuboid and Cube Ex 18.1
- RD Sharma Class 9 Solutions Chapter 18 Surface Areas and Volume of a Cuboid and Cube Ex 18.2
- RD Sharma Class 9 Solutions Chapter 18 Surface Areas and Volume of a Cuboid and Cube VSAQS
- RD Sharma Class 9 Solutions Chapter 18 Surface Areas and Volume of a Cuboid and Cube MCQS

Mark correct alternative in each of the following:

Question 1.

The length of the longest rod that can be fitted in a cubical vessel of edge 10 cm long, is

(a) 10 cm

(b) 10\(\sqrt { 2 } \) cm

(c) 10\(\sqrt { 3 } \) cm

(d) 20 cm

Solution:

Edge of cuboid (a) = 10 cm

∴ Longest edge = \(\sqrt { 3 } \) a cm

= \(\sqrt { 3 } \) x 10 = 10\(\sqrt { 3 } \) cm (c)

Question 2.

Three equal cubes are placed adjacently in a row. The ratio of the total surface area of the resulting cuboid to that of the sum of the surface areas of three cubes, is

(a) 7 : 9

(b) 49 : 81

(c) 9 : 7

(d) 27 : 23

Solution:

Let a be the side of three equal cubes

∴ Surface area of 3 cubes

= 3 x 6a^{2} = 18a^{2}

and length of so formed cuboid = 3a

Breadth = a

and height = a

∴ Surface area = 2(lb + bh + hl)

= 2[3a x a + a x a+a x 3a] = 2[3a^{2} + a^{2} + 3a^{2}] = 2 x 7a^{2} = 14a^{2}

∴ Ratio in the surface areas of cuboid and three cubes = 14a^{2} : 18a^{2}= 7:9 (a)

Question 3.

If the length of a diagonal of a cube is 8 \(\sqrt { 3 } \) cm, then its surface area is

(a) 512 cm^{2}

(b) 384 cm^{2}

(c) 192 cm^{2}

(d) 768 cm^{2}

Solution:

Length of the diagonal of cube = 8 \(\sqrt { 3 } \) cm

Question 4.

If the volumes of two cubes are in the ratio 8:1, then the ratio of their edges is

(a) 8 : 1

(b) 2\(\sqrt { 2 } \) : 1

(c) 2 : 1

(d) none of these

Solution:

Let volume of first cube = 8x^{3}

and of second cube = x^{3}

Question 5.

The volume of a cube whose surface area is 96 cm^{2}, is

(a) 16\(\sqrt { 2 } \) cm^{3}

(b) 32 cm^{3}

(c) 64 cm^{3}

(d) 216 cm^{3}

Solution:

Surface area of a cube = 96 cm^{2}

Question 6.

The length, width and height of a rectangular solid are in the ratio of 3 : 2 : 1. If the volume of the box is 48 cm^{3}, the total surface area of the box is

(a) 27 cm^{2}

(b) 32 cm^{2}

(c) 44 cm^{2}

(d) 88 cm^{2}

Solution:

Ratio in the dimensions of a cuboid =3 : 2 : 1

Let length = 3x

Breadth = 2x

and height = x

Then volume = lbh = 3x x 2x x x = 6×3

∴ 6x^{3} = 48 ⇒ x^{3}= \(\frac { 48 }{ 6 }\) = 8 = (2)^{3}

∴ x = 2

∴ Length (l) = 3 x 2 = 6 cm

Breadth (b) = 2 x 2 = 4 cm

Height (h) = 1 x 2 = 2 cm

Now surface area = 2[lb + bh + hl]

= 2[6 x 4 + 4 x 2 + 2 x 6] cm^{2}

= 2[24 + 8-+ 12] = 2 x 44 cm^{2}

= 88 cm^{2} (d)

Question 7.

If the areas of the adjacent faces of a rectangular block are in the ratio 2:3:4 and its volume is 9000 cm3, then the length of the shortest edge is

(a) 30 cm

(b) 20 cm

(c) 15 cm

(d) 10 cm

Solution:

Ratio in the areas of three adjacent faces of a cuboid = 2 : 3 : 4

Volume = 9000 cm^{3}

Let the area of faces be 2x, 3x, Ax and

Let a, b, and c be the dimensions of the cuboid, then

∴ 2x = ab, 3x = be, 4x = ca

∴ ab x be x ca = 2x x 3x x 4x

a^{2}b^{2}c^{2} = 24 x 3

But volume = abc = 9000 cm^{3}

Question 8.

If each edge of a cube, of volume V, is doubled, then the volume of the new cube is

(a) 2V

(b) 4V

(c) 6V

(d) 8V

Solution:

Let a be the edge of a cube whose Volume = V

∴ a3 = V

By doubling the edge, we get 2a

Then volume = (2a)3 = 8a^{3}

∴ Volume of new cube = 8a^{3} = 8V (d)

Question 9.

If each edge of a cuboid of surface area S is doubled, then surface area of the new cuboid is

(a) 2S

(b) 4S

(c) 6S

(d) 8S

Solution:

Let each edge of a cube = a

Then surface area = 6a^{2}

∴ S = 6a^{2}

Now doubling the edge, we get

New edge of a new cube = 2a

∴ Surface area = 6(2a)^{2}

= 6 x 4a^{2} = 24a^{2}

= 4 x 6a^{2} = 4S (b)

Question 10.

The area of the floor of a room is 15 m2. If its height is 4 m, then the volume of the air contained in the room is

(a) 60 dm^{3}

(b) 600 dm^{3}

(c) 6000 dm^{3}

(d) 60000 dm^{3}

Solution:

Area of a floor of a room = 15 m^{2}

Height (h) = 4 m

∴ Volume of air in the room = Floor area x Height

= 15 m^{2} x 4 m = 60 m^{3}

= 60 x 10 x 10 x 10 dm^{2} = 60000 dm^{2} (d)

Question 11.

The cost of constructing a wall 8 m long, 4 m high and 20 cm thick at the rate of ₹25 per m^{3} is

(a) ₹16

(b) ₹80

(c) ₹160

(d) ₹320

Solution:

Length of wall (l) = 8 m

Breadth (b) = 20 cm = \(\frac { 1 }{ 5 }\) m

Height (h) = 4 m

Question 12.

10 cubic metres clay in uniformaly spread on a land of area 10 acres. The rise in the level of the ground is

(a) 1 cm

(b) 10 cm

(c) 100 cm

(d) 1000 cm

Solution:

Volume of clay = 10 m^{3}

Area of land = 10 acres

= 10 x 100 = 1000 m^{2}

∴ Rise of level by spreading the clay

Question 13.

Volume of a cuboid is 12 cm^{3}. The volume (in cm^{3}) of a cuboid whose sides are double of the above cuboid is

(a) 24

(b) 48

(c) 72

(d) 96

Solution:

Volume of cuboid = 12 cm^{3}

By doubling the sides of the cuboid the

volume will be = 12 cm^{3} x 2 x 2 x 2

= 96 cm^{3} (d)

Question 14.

If the sum of all the edges of a cube is 36 cm, then the volume (in cm3) of that cube is

(a) 9

(b) 27

(c) 219

(d) 729

Solution:

Sum of all edges of a cube = 36 cm

No. of edge of a cube are 12

∴ Length of its one edge = \(\frac { 36 }{ 12 }\) = 3 cm

Then volume = (edge)^{3} = (3)^{3} cm^{3}

= 27 cm^{3} (b)

Question 15.

The number of cubes of side 3 cm that can be cut from a cuboid of dimensions 9 cm x 9 cm x 6 cm, is

(a) 9

(b) 10

(c) 18

(d) 20

Solution:

Dimensions of a cuboid = 9 cm x 9 cm x 6 cm

Question 16.

On a particular day, the rain fall recorded in a terrace 6 m long and 5 m broad is 15 cm. The quantity of water collected in the terrace is

(a) 300 litres

(b) 450 litres

(c) 3000 litres

(d) 4500 litres

Solution:

Dimension of a terrace = 6mx5m

Level of rain on it = 15 cm

∴ Volume of water collected on it

Question 17.

If A_{1}, A_{2} and A_{3} denote the areas of three adjacent faces of a cuboid, then its volume is

Solution:

Let l, b, h be the dimensions of the cuboid

∴ A_{1}= lb, A_{2} = bh, A_{3} = hl

∴ A_{1} A_{2} A_{3} = lb.bh.hl = l_{2}b_{2}h_{2}

Question 18.

If l is the length of a diagonal of a cube of volume V, then

Solution:

Volume of a cube = V

and longest diagonal = l

Question 19.

If V is the volume of a cuboid of dimensions x, y, z and A is its surface area, then \(\frac { A }{ V }\)

Solution:

A is surface area, V is volume and x, y and z are the dimensions

Then V = xyz

A = 2[xy + yz + zx]

Question 20.

The sum of the length, breadth and depth of a cuboid is 19 cm and its diagonal is 5\(\sqrt { 5 } \) cm. Its surface area is

(a) 361 cm^{2}

(b) 125 cm^{2}

(c) 236 cm^{2}

(d) 486 cm^{2}

Solution:

Let x, y, z be the dimensions of a cuboid,

then x + y + z = 19 cm

Question 21.

If each edge of a cube is increased by 50%, the percentage increase in its surface area is

(a) 50%

(b) 75%

(c) 100%

(d) 125%

Solution:

Let in first case, edge of a cube = a

Then surface area = 6a^{2}

In second case, increase in side = 50%

Question 22.

A cube whose volume is 1/8 cubic centimeter is placed on top of a cube whose volume is. 1 cm^{3}. The two ,cubes are then placed on top of a third cube whose volume is 8 cm^{3}. The height of the stacked cubes is

(a) 3.5 cm

(b) 3 cm

(c) 7 cm

(d) none of these

Solution:

Volume of first cube = \(\frac { 1 }{ 2 }\) cm^{3}

Hope given RD Sharma Class 9 Solutions Chapter 18 Surface Areas and Volume of a Cuboid and Cube MCQS are helpful to complete your math homework.

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