ABC26GN5009 · Volume and Surface Area
Subject: General Aptitude · Chapter: Volume and Surface Area · Exam: · Marks: · Difficulty:
If a solid sphere of radius 10 cm is moulded into 8 spherical solid balls of equal radius, then the surface area of each ball is
(a)$50 \pi \mathrm{cm}^{2}$
(b)$60 \pi \mathrm{cm}^{2}$
(c)$75 \pi \mathrm{cm}^{2}$
(d)$100 \pi \mathrm{cm}^{2}$
Answer
Explanation
Volume of each ball $=\frac{1}{8} \times\left(\frac{4}{3} \pi \times 10 \times 10 \times 10\right) \mathrm{cm}^{3}$. Let the radius of each ball be $r \mathrm{cm}$. Then, $\frac{4}{3} \pi r^{3}=\frac{1}{8} \times\left(\frac{4}{3} \pi \times 10 \times 10 \times 10\right) \Rightarrow r^{3}=\left(\frac{10}{2}\right)^{3}=5^{3}$ $$\Rightarrow r=5 .$$ ∴ Surface area of each ball $=4 \pi r^{2}=\left[4 \pi \times(5)^{2}\right] \mathrm{cm}^{2}$ $$=(100 \pi) \mathrm{cm}^{2} .$$
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