Subject: General Aptitude · Chapter: Volume and Surface Area · Exam: 2016 · Marks: · Difficulty:
If the radius of a sphere is increased by 10\%, then the volume will be increased by
(a)33.1\%
(b)30\%
(c)50\%
(d)10\%
Answer
Answer (as printed): A
Explanation
If $R$ is the radius of sphere, volume of the sphere $=\frac{4}{3} \pi R^{3}$. When radius of sphere is increased by $10 \%$. New volume $=\frac{4}{3} \pi(1.1 R)^{3}$ $$=\frac{4}{3} \pi R^{3}(1.331)$$ Difference $=\frac{4}{3} \pi R^{3}(1.331)-\frac{4}{3} \pi R^{3}=\frac{4}{3} \pi R^{3}(1.331-1)$ $$=\frac{4}{3} \pi R^{3}(0.331)$$ Increase $\%=\frac{\frac{4}{3} \pi R^{3}(0.331)}{\frac{4}{3} \pi R^{3}} \times 100=33.1 \%$
Explanation as extracted from the printed page; notation may be imperfect.