A solid metal cuboid with dimension 10 cm, 11 cm and 8 cm is melted and identical solid spheres, each of radius 1 cm, are formed. The number of sphere formed is :

1. 105

2. 210

3. 315

4. 420

By applying force on an uniform metallic wire, the wire is extended four times along its length with same width all around. Then :

(i) The volume of metal in both the cases is same.

(ii) The surface area of solid wires in both the cases is same.

Which of the above statements is/are true?

1. only (i)

2. only (ii)

3. both (i) and (ii)

4. neither (i) nor (ii)

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.