Volume & Surface Area of Solids — Assertion-Reason Type Questions

Assertion (A) : The length of the longest rod that can be put in a room of dimensions 10 m × 10 m × 5 m is 15 m.

Reason (R) : Length of the diagonal of a cuboid = $\sqrt{l^2 + b^2 + h^2}$

1. A is true, R is false

2. A is false, R is true

3. Both A and R are true

4. Both A and R are false

Answer

Given,

Room dimensions = 10 m × 10 m × 5 m

The longest rod that can be placed in a room = Diagonal of room.

We know that,

Diagonal of cuboid = $\sqrt{l^2 + b^2 + h^2}$

Diagonal of room = $\sqrt{10^2 + 10^2 + 5^2}$

= $\sqrt{100 + 100 + 25}$

= $\sqrt{225}$

= 15 m.

So length of the longest rod that can be placed in the room = 15 m.

∴ Assertion (A) is true.

By formula,

Length of the diagonal of cuboid = $\sqrt{l^2 + b^2 + h^2}$

∴ Reason (R) is true.

Both Assertion (A) and Reason (R) are true.

Hence, option 3 is the correct option.

Assertion (A) : The perimeter of one face of a cube is 20 cm. Its volume is 64 cm³.

Reason (R) : Volume of a cube of edge a is given by a³.

1. A is true, R is false

2. A is false, R is true

3. Both A and R are true

4. Both A and R are false

Answer

Given,

Perimeter = 20 cm

Each face of a cube is a square.

Let the side of square be a cm.

Perimeter of a square = 4 × side.

⇒ 20 = 4a

⇒ a = $\dfrac{20}{4}$

⇒ a = 5 cm.

Calculating the volume of a cube,

Volume of cube = a³

= 5³

= 125 cm³.

∴ Assertion (A) is false.

Given,

Edge of a cube = a

By formula,

Volume of a cube = a³

∴ Reason (R) is true.

Assertion (A) is false, Reason (R) is true.

Hence, option 2 is the correct option.