ABC26GN5010 · Volume and Surface Area
Subject: General Aptitude · Chapter: Volume and Surface Area · Exam: · Marks: · Difficulty:
A hollow spherical metallic ball has an external diameter 6 cm and is $\frac{1}{2} \mathrm{cm}$ thick. The volume of metal used in the ball is
(a)$37 \frac{2}{3} \mathrm{cm}^{3}$
(b)$40 \frac{2}{3} \mathrm{cm}^{3}$
(c)$41 \frac{2}{3} \mathrm{cm}^{3}$
(d)$47 \frac{2}{3} \mathrm{cm}^{3}$
Answer
Explanation
External radius $=3 \mathrm{cm}$, Internal radius $=(3-0.5) \mathrm{cm}=2.5 \mathrm{cm}$. Volume of the metal $=\left[\frac{4}{3} \times \frac{22}{7} \times\left\{(3)^{3}-(2.5)^{3}\right\}\right] \mathrm{cm}^{3}$ $$=\left(\frac{4}{3} \times \frac{22}{7} \times \frac{91}{8}\right) \mathrm{cm}^{3}=\left(\frac{143}{3}\right) \mathrm{cm}^{3}=47 \frac{2}{3} \mathrm{cm}^{3} .$$
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