Question : The largest possible right circular cylinder is cut out from a wooden cube of edge 7 cm. Find the volume of the cube (in cm3) left over after cutting the cylinder. (Use $\pi=\frac{22}{7}$)
Option 1: 73.5
Option 2: 63.5
Option 3: 87.5
Option 4: 67.5
Correct Answer: 73.5
Solution :
The largest possible right circular cylinder that can be cut out from a cube will have its diameter equal to the edge of the cube.
Given that the edge of the cube is 7 cm, the radius $r$ of the cylinder is $\frac{7}{2}$ cm and the height $h$ of the cylinder is also 7 cm.
The volume of the cylinder, $V_1=\pi r^2 h = \pi \left(\frac{7}{2}\right)^2 \times 7 = \frac{22}{7} \times \frac{49}{4} \times 7 =269.5\;\text{cm}^3$
The volume of the cube is $s^3$, where $s$ is the edge of the cube.
$V_2 = 7^3=343\;\text{cm}^3$
The volume of the cube left over after cutting the cylinder = $V_2 - V_1$ = 343 – 269.5 = 73.5 cm
3
Hence, the correct answer is 73.5.
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