Question

A clown’s cap is in the form of a right circular cone of radius 7cm and height 24cm. Find the area of the sheet required to make 10 such caps.

Answer 1

Hint: Find the slant height of the cone. Use the fact that the slant height of the cone is given by $l=\sqrt{{{h}^{2}}+{{r}^{2}}}$. Hence find the slant of the cone. Use the fact that the curved surface area of the cone is given by $A=\pi rl$. Hence determine the area of one cap. Hence determine the area of 10 caps and hence find the total area of the sheet required to make the caps.

Complete step-by-step answer:

Here the radius of the cone = 7cm and the height of the cone = 24cm.
We know that the slant height of the cone is given by $l=\sqrt{{{h}^{2}}+{{r}^{2}}}$
Hence, we have
$l=\sqrt{{{7}^{2}}+{{24}^{2}}}=25$
Hence the slant height of the cone is 25cm.
We know that the curved surface area of a cone is given by $A=\pi rl$
Hence, we have
The curved surface area of the cap $=\pi rl=\pi \times 7\times 25$
Using $\pi =\dfrac{22}{7}$, we get
The curved surface area of the cap $=\dfrac{22}{7}\times 7\times 25=550$.
Hence the curved surface area of the cap is 550 square centimetres.
Hence the area of the sheet required to make one cap 550 square centimetres.
Hence the area of the sheet required to make 10 caps $=550\times 10$= 5500 square centimetres.

Note: In mensuration problems, special care should be taken about the units. When comparing things or finding area/ volume, units should be kept the same. Many students do not change the units or make them the same and end up with incorrect results.