2021 · Q78
Consider the following for the next three (03) items that follow : A solid consisting of a right circular cone of radius x and height 2x standing on a hemisphere of radius x (take π = 22/7). The solid is placed upright in a right circular cylinder full of water such that it touches the bottom. If the internal radius of cylinder is x and height is 3x, what is the approximate volume of water left in the cylinder ?
Elementary MathematicsMensuration
- A5.04x³
- B5.09x³
- C5.14x³
- D5.24x³
Explanation
Cylinder volume = πx²·3x = 3πx³; solid volume = (4/3)πx³ (from Q76). Water left = 3πx³ − (4/3)πx³ = (5/3)πx³ = (5/3)(22/7)x³ = 110x³/21 ≈ 5.238x³. The nearest option is (d) 5.24x³.