Question

The adjoining figure shows the measure of a Joker’s cap. How much cloth is needed to make such a cap?

Answer 1

Hint: To find the amount of the cloth we will find the curved surface area of the cone using formula \[\pi rl\] where \[\pi {\text{ is }}\dfrac{{22}}{7}\], r is radius and l is slant height.

Complete step by step solution:
In the question we are given the shape and dimension of a Joker's cap and we have to find the amount of cloth required to make a cap.
As the figure is given in the question,

Now here we are given the length of radius which is 10cm and slant height which is 21cm. This means that r is equal to 10cm and l is 21cm as radius is represented by r and slant height as l.
Now to find the amount of cloth we have to find the curved surface area from the given dimensions.
For the cone, the formula of curved surface is \[\pi rl\] here r is radius, l is slant height and \[\pi \] is taken as value \[\dfrac{{22}}{7}.\]
Now substituting the value of radius and slant height as 10cm and 21cm respectively, so we get, curved surface area as,
\[\dfrac{{22}}{7}rl{\text{ or }}\dfrac{{22}}{7} \times 10cm \times 21cm\]
So the curved surface area is\[22 \times 10 \times 3{\text{ or 660c}}{{\rm{m}}^{\rm{2}}}\].
Hence, the amount of cloth required to make a cap is \[660c{m^2}\].

Note: Students while solving generally find total surface area instead of curved surface area as they miss out the fact that for measurement of cloth base area shall be exchanged.