A hollow sphere has a volume of kcm3 and a surface area of kcm2. Calculate the diameter of the sphere.
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Correct Answer: Option B
Explanation:
\(Volume = \frac{4}{3} \pi r^3 = k\) ...(i)
\(S.A = 4\pi r^2 = k\) ... (ii)
Divide (i) by (ii),
\(\frac{4}{3} \pi r^3 \div 4\pi r^2 = \frac{k}{k}\)
\(\frac{r}{3} = 1 \implies r = 3cm\)
Diameter = 2 x 3cm = 6cm
\(Volume = \frac{4}{3} \pi r^3 = k\) ...(i)
\(S.A = 4\pi r^2 = k\) ... (ii)
Divide (i) by (ii),
\(\frac{4}{3} \pi r^3 \div 4\pi r^2 = \frac{k}{k}\)
\(\frac{r}{3} = 1 \implies r = 3cm\)
Diameter = 2 x 3cm = 6cm