Question

Suppose that there is a conical strainer as shown in the given figure. The radius of its broadest end is 6 cm and length is 8 cm. Now if 2 ${cm}^2$ of strainer has an average of 8 tiny holes. Then find the total number of holes in the entire strainer.

Answer 1

Since holes are in the curved surface area of cone, we first have to find the curved surface area of the strainer.

Slant height, l = $\sqrt[2]{2\left(r^2\right)+\left(h^2\right)}$ = $\sqrt[2]{2\left(6^2\right)+\left(8^2\right)}$
= 10 cm
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Curved surface area of the cone
$=\pi rl=\pi \times 6\times 10=60\pi {cm}^2$
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Since it is given that 2 cm${}^2$ area of strainer has 8 holes, 1 cm${}^2$ area of the strainer must have 4 holes.

Hence, the total number of holes in the entire strainer (i.e., 60 $\pi c{m}^2$)
$=60\times \pi \times 4=240\times \frac{22}{7}=754.3\text{or}754\text{approx.}$
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