The base radius of two right circular cone of the same height are in ratio 3 : 5.

Assertion(A): The ratio between their volume is 9 : 25.

Reason(R): As

$\dfrac{r$1}{r2} = \dfrac{3}{5} \\[1em] \dfrac{πr1^2h}{πr2^2h} = \dfrac{r1^2}{r2^2} = \Big(\dfrac{3}{5}\Big)^2 \\[1em]

1. A is true, R is false.

2. A is false, R is true.

3. Both A and R are true and R is correct reason for A.

4. Both A and R are true and R is incorrect reason for A.

A solid cone of height 3 cm and radius 3 cm is recast into solid cylinder each of height 1 cm and radius 1 cm.

Assertion(A): Number of cylinders formed = $\dfrac{1}{3}$ x 3 x 3 x 3

Reason(R): Number of cylinders formed = $\dfrac{\dfrac{1}{3}π(3)^2 \times 3}{π(1)^2 \times 1}$

1. A is true, R is false.

2. A is false, R is true.

3. Both A and R are true and R is correct reason for A.

4. Both A and R are true and R is incorrect reason for A.

A solid sphere of radius 6 cm is melted and recast into solid spheres of diameter 2 cm each.

Statement (1): The number of solid sphere formed is 6 x 6 x 6 = 216.

Statement (2): If the smaller spheres formed are identical, the number of solid sphere formed = $\dfrac{\text{Volume of sphere melted}}{\text{Volume of each of the sphere formed}}$

1. Both the statement are true.

2. Both the statement are false.

3. Statement 1 is true, and statement 2 is false.

4. Statement 1 is false, and statement 2 is true.

Water in a canal 6 m wide and 2 m deep, is flowing with the speed of 18 km/h.

Statement (1): The volume of water that flows through the canal in 20 minutes = 6 x 2 x $\Big(18 \times \dfrac{5}{18}\Big)$ x 20 x 60 m³.

Statement (2): The volume of water that flows through the canal = 6 x 2 x 18 x 20 m³.

1. Both the statement are true.

2. Both the statement are false.

3. Statement 1 is true, and statement 2 is false.

4. Statement 1 is false, and statement 2 is true.