A solid wooden cylinder is of height h cm and radius r cm. A conical cavity of same height and the same radius is drill out of the solid cylinder.

Statement (1): The volume of the remaining wood = volume of the solid cylinder - volume of the cone drilled.

Statement (2): The volume of the remaining wood = πr²h - $\dfrac{1}{3}$ πr²h = $\dfrac{2}{3}$ πr²h

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.

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.

What is the least number of solid metallic spheres, each of 6 cm diameter, that should be melted and recast to form a solid metal cone whose height is 45 cm and diameter 12 cm ?

A largest sphere is to be carved out of a right circular cylinder of radius 7 cm and height 14 cm. Find the volume of the sphere.
(Answer correct to the nearest integer)