RD Sharma 2020 solution class 9 chapter 18 Surface Area and Volume of a Cuboid and Cube MCQS

MCQS

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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

Answer 1:

The longest rod that can be fitted in the cubical vessel is its diagonal.

Side of the cube

So, the diagonal of the cube,

So, the length of the longest rod that can be fitted in the cubical box is.

Hence, the correct choice is (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

Answer 2:

Let, Side of each cube

So, the dimensions of the resulting cuboid are,

Length

Breadth

Height

Total surface area of the cuboid,

Sum of the surface areas of the three cubes,

Required ratio,

Thus, the required ratio is.

Hence the correct choice is (a).

Question 3:

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

(a) 512 cm²

(b) 384 cm²

(c) 192 cm²

(d) 768 cm²

Answer 3:

Let,

Side of the cube

Length of the diagonal

We have to find the surface area of the cube

Surface area of the cube,

Thus, surface area of the cube is.

Hence, the correct choice is (b).

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

Answer 4:

Let,

Volumes of the two cubes

Edges of the two cubes

We know that,

So,

Ratio of their edges is.

So, the correct choice is (c).

Question 5:

The volume of a cube whose surface area is 96 cm², is

(a) $16\sqrt{2}c{m}^3$

(b) 32 cm³

(c) 64 cm³

(d) 216 cm³
 

Answer 5:

Let,

Side of the cube

Volume of the cube

Surface area of the cube

We have,

So,

Thus, volume of the cube is.

Hence the correct choice is (c).

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 48cm³, the total surface area of the box is

(a) 27 cm²

(b) 32 cm²

(c) 44 cm²

(d) 88 cm²

Answer 6:

Length (l), width (b) and height (h) of the rectangular solid are in the ratio 3 : 2 : 1.

So we can take,

We need to find the total surface area of the box

Volume of the box,

Thus,

Surface area of the box,

Thus total surface area of the box is.

Hence, the correct option is (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

Answer 7:

Let, the edges of the cuboid be a cm, b cm and c cm.

And, a < b < c

The areas of the three adjacent faces are in the ratio 2 : 3 : 4.

So,

ab : ca : bc = 2 : 3 : 4, and its volume is 9000 cm³

We have to find the shortest edge of the cuboid

Since;

Similarly,

Volume of the cuboid,

As and

Thus, length of the shortest edge is.

Hence; the correct choice is (c).

Question 8:

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

(a) 2 V

(b) 4 V

(c) 6 V

(d) 8 V

Answer 8:

Let, Initial edge of the cube

So,

In the new cube, let,

Edge of new cube

Volume of the new cube,

Volume of the new cube is.

Hence, the correct choice is (d).

Question 9:

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

(a) 2 S

(b) 4 S

(c) 6 S

(d) 8 S

Answer 9:

Let,

Length of the first cuboid

Breadth of the first cuboid

Height of the first cuboid

And,

Length of the new cuboid

Breadth of the new cuboid

Height of the new cuboid

We know that,

Surface area of the first cuboid,

Surface area of the new cuboid,

The surface area of the new cuboid is.

So, the correct choice is (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 dm³

(b) 600 dm³

(c) 6000 dm³

(d) 60000 dm³

Answer 10:

The area of the floor

Height of the room

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

So, capacity of the room to contain air,

Volume of the air contained in the room is.

So the correct choice is (d).

Question 11:

The cost of constructing a wall 8 m long, 4 m high and 10 cm thick at the rate of Rs. 25 per m³ is

(a) Rs. 16

(b) Rs. 80

(c) Rs. 160

(d) Rs. 320

Answer 11:

Dimensions of the wall are,

Length

Breadth

Height

Volume of the hall,

Cost of building the wall at the rate of Rs. 25/m³,

The cost of building the wall is.

Hence, the correct option is (c).

Question 12:

10 cubic metres clay is uniformly spread on a land of area 10 ares. the rise in the level of the ground is

(a) 1 cm

(b) 10 cm

(c) 100 cm

(d) 1000 cm

Answer 12:

Volume of the clay to be spread,

Area on which the clay is spread

Let,

Rise in the level of the ground

We know that,

Rise in the level of the ground is.

Hence, the correct option is (a).

Question 13:

Volume of a cuboid is 12 cm3. The volume (in cm3) of a cuboid whose sides are double of the above cuboid is

(a) 24

(b) 48

(c) 72

(d) 96

Answer 13:

Let,

Length of the first cuboid

Breadth of the first cuboid

Height of the first cuboid

Volume of the cuboid is 12 cm³

Dimensions of the new cuboid are,

Length

Breadth

Height

We are asked to find the volume of the new cuboid

We know that,

Volume of the new cuboid,

Thus volume of the new cuboid is.

Hence, the correct option is (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

Answer 14:

A cube has total 12 edges.

Let, edge of the cube

Sum of all the edges of the cube = 12a

Volume of that cube,

Volume of the cube is.

Hence, the correct option is (b).

Question 15:

The number of cubes of side 3 cm that can be cut from a cuboid of dimensions 10 cm × 9 cm × 6 cm, is

(a) 9

(b) 10

(c) 18

(d0 20

Answer 15:

We have the cuboid of dimensions.

We are to find how many cubs with edge 3 cm can be cut from the given cuboid

Let us cut this cuboid into following two cuboids

And

So the number of cubes of side 3 cm, that can be cut from the first cuboid,

We can not cut a single cube of side 3 cm from the second cuboid of dimension

Hence this much volume is useless for us.

So, we can cut maximum cubes of side 3 cm from the cuboid of dimensions.

Hence, the correct option is (c).

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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

Answer 16:

Length of the terrace,

Breadth of the terrace,

Height of the water level

We have to find the quantity of water

Quantity of water,

The quantity of water is.

The correct option is (d).

 

Question 17:

If A1, A2, and A3 denote the areas of three adjacent faces of a cuboid, then its volume is

(i) A1 A2 A3

(ii) 2A1 A2 A3

(iii) $\sqrt{A_1{A}_2{A}_3}$

(iv) ${}^3\sqrt{A_1{A}_2{A}_3}$

Answer 17:

We have;

Here A₁, A₂ and A₃ are the areas of three adjacent faces of a cuboid.

But the areas of three adjacent faces of a cuboid are lb, bh and hl, where,

Length of the cuboid

Breadth of the cuboid

Height of the cuboid

We have to find the volume of the cuboid

Here,

Thus, volume of the cuboid is.

Hence, the correct choice is (c).

Question 18:

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

(a) 3V = l³

(b) $\sqrt{3}V=l^3$

(c) $3\sqrt{3}V=2l^3$

(d) $3\sqrt{3}V=l^3$

Answer 18:

We have,

Diagonal of the cube

Volume of the cube

Side of the cube

We know that,

So, the correct choice is (d).

Question 19:

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

(a) x²y²z²

(b) $\frac{1}{2}\left(\frac{1}{xy}+\frac{1}{yz}+\frac{1}{zx}\right)$

(c) $\left(\frac{1}{x}+\frac{1}{y}+\frac{1}{z}\right)$

(d) $\frac{1}{xyz}$

Answer 19:

Dimensions of the cuboid are.

So, the surface area of the cuboid

Volume of the cuboid

Hence, the correct choice is (c).

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 cm²

(b) 125 cm²

(c) 236 cm²

(d) 486 cm²

Answer 20:

Let,

Length of the cuboid

Breadth of the cuboid

Height of the cuboid

We have,

, diagonal of the cuboid

We are asked to find the surface area

So, the surface area,

Thus, the surface area is

Hence, the correct choice is (c).

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%

Answer 21:

Let,

Initial edge of the cube

Initial surface area of the cube

Increased edge of the cube

Increased surface area of the cube

We have to find the percentage increase in the surface area of the cube

Since it’s given that

We have,

Percentage increase in surface area,

Increase in surface area is.

Hence, the correct choice is (d).

Question 22:

A cube whose volume is 1/8 cubic centimeter is placed on top of a cube whose volume is 1 cm³. The two cubes are then placed on top of a third cube whose volume is 8 cm³. The height of the stacked cubes is

(a) 3.5 cm

(b) 3 cm

(c) 7 cm

(d) none of these

Answer 22:

Let,

Volumes of the three cubes

Sides of the three cubes

We know that,

So,

Similarly,

And;

So the height of the resulting structure,

The height of the structure is.

Hence, the correct choice is (a).