In this chapter, we provide RD Sharma Solutions for Chapter 18 Surface Areas and Volume of a Cuboid and Cube MCQs for English medium students, Which will very helpful for every student in their exams. Students can download the latest RD Sharma Solutions for Chapter 18 Surface Areas and Volume of a Cuboid and Cube MCQs Maths pdf, free RD Sharma Solutions for Chapter 18 Surface Areas and Volume of a Cuboid and Cube MCQs Maths book pdf download. Now you will get step by step solution to each question.

Textbook | NCERT |

Class | Class 9 |

Subject | Maths |

Chapter | Chapter 18 |

Chapter Name | Surface Areas and Volume of a Cuboid and Cube |

Exercise | MCQs |

**RD Sharma Solutions for Class 9 Chapter 18 Surface Areas and Volume of a Cuboid and Cube MCQs Download PDF**

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) 102–√ cm

(c) 103–√ cm

(d) 20 cm

Solution:

Edge of cuboid (a) = 10 cm

∴ Longest edge = 3–√ a cm

= 3–√ x 10 = 103–√ 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 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 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) 22–√ : 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) 162–√ 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}= 486 = 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 = 15 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 = 3612 = 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 AV

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 55–√ 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 = 12 cm^{3}

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