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 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
Updated On: Sep 26, 2024
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The Correct Option is C
Solution and Explanation
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 \(h + a + R = 3 + 1 + 2 = 6.\)
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