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The ratio of the base area of a hollow cone to that of its curved...

Mathematics
NECO 2008

The ratio of the base area of a hollow cone to that of its curved surface is 1:4. If its base radius is 7cm, calculate the slant height of the cone

  • A. 7cm
  • B. 22cm
  • C. 28cm
  • D. 49cm
  • E. 154cm
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Correct Answer: Option C
Explanation

The base of a cone is a circle, r = 7cm

Base area of a cone = \(\pi\)r\(^2\)

Curve surface area of a cone = \(\pi\)l

\(\pi\)r\(^2\) :  \(\pi\)l = 1 : 4

\(\frac{\pi r^2}{\pi l}\) = \(\frac{1}{4}\)

\(\frac{r}{l} = \frac{1}{4}\)

\(\frac{7}{l} =  \frac{1}{4}\)

cross multiplying 

l = 4 x 7 = 28cm.


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