Question

A ball of diameter 4 cm is kept on top of a hollow cylinder standing vertically. The height of the cylinder is 3 cm, while its volume is $9 \pi cm^3$ . Then the vertical distance, in cm, of the topmost point of the ball from the base of the cylinder is

• A. 2
• B. 8
• C. 6
• D. 4

Answer 1

Answer: (C)

6

Answer 2

The height of the cylinder (h) is 3.
The volume is $9\pi$, and using the formula for the volume of a cylinder $(\pi r²h = 9\pi),$ we find that the radius (r) is $\sqrt{3}.$
The radius of the ball (R) is 2.
The height of O, the centre of the ball, above the line representing the top of the cylinder is denoted as 'a'$(a = 1).$
Therefore, the height of the topmost point of the ball from the base of the cylinder is $h + a + R = 3 + 1 + 2 = 6.$