Question : Find the volume of the largest right circular cone that can be cut out from a cube whose edge is $3 \frac{1}{2}$ cm, correct to two places of decimals (use $\pi=\frac{22}{7}$).
Option 1: $13.21 \mathrm{~cm}^3$
Option 2: $21.31 \mathrm{~cm}^3$
Option 3: $11.23 \mathrm{~cm}^3$
Option 4: $12.13 \mathrm{~cm}^3$
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Correct Answer: $11.23 \mathrm{~cm}^3$
Solution :
Given:
The edge of the cube = $3\frac{1}{2}=\frac{7}{2}$ cm, this will be the altitude of the cone, $h$.
Now, the radius of the circular cone $=r=\frac{\frac{7}{2}}{2}=\frac{7}{4}$
The volume of cone, V = $\frac{1}{3}\pi r^2h$
⇒ V = $\frac{1}{3}×\frac{22}{7}×\frac{7}{4}×\frac{7}{4}×\frac{7}{2}$
⇒ V = $\frac{539}{48}$
⇒ V = 11.23 cm
3
Hence, the correct answer is 11.23 cm
3
.
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