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A hollow sphere has a volume of kcm3 and a surface area of kcm2. Calculate...

Mathematics
WAEC 1995

A hollow sphere has a volume of kcm3 and a surface area of kcm2. Calculate the diameter of the sphere.

  • A. 3cm
  • B. 6cm
  • C. 9cm
  • D. 12cm
  • E. More information is needed
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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


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