ABC26GN5037 · Volume and Surface Area

Subject: General Aptitude · Chapter: Volume and Surface Area · Exam: 2011 · Marks: · Difficulty:

A cone of height 15 cm and base diameter 30 cm is carved out of a wooden sphere of radius 15 cm. The percentage of wood wasted is
(a)25\%
(b)40\%
(c)50\%
(d)75\%
Answer
Answer (as printed): D
Explanation
Volume of sphere $=\left(\frac{4}{3} \pi \times 15 \times 15 \times 15\right) \mathrm{cm}^{3}$. $$\text { Volume of cone }=\left(\frac{1}{3} \pi \times 15 \times 15 \times 15\right) \mathrm{cm}^{3} .$$ Volume of wood wasted = $$\begin{aligned} & {\left[\left(\frac{4}{3} \pi \times 15 \times 15 \times 15\right)-\left(\frac{1}{3} \pi \times 15 \times 15 \times 15\right)\right] \mathrm{cm}^{3} .} \\ & \quad=(\pi \times 15 \times 15 \times 15) \mathrm{cm}^{3} . \\ & \therefore \text { Required percentage }=\left(\frac{\pi \times 15 \times 15 \times 15}{\frac{4}{3} \pi \times 15 \times 15 \times 15} \times 100\right) \%=75 \% . \end{aligned}$$

Explanation as extracted from the printed page; notation may be imperfect.

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