Question

A joker cap is in the form of a right circular cone of radius $ 7cm, $ $ l = 25cm, $ find the area of the sheet required for $ 12 $ such caps.

Answer 1

Hint: Let us define the right circular cone; which is the one whose axis is in the form of perpendicular to the plane from the given base.
We can also generate the right cone just by revolving a right triangle of one of the legs; they are more similar.
For the right circular cone, the radius is given as seven centimeters and also the length is given as twenty-five centimeters.
Formula used: $ \pi rl $ is the area of the curved surface, where r is the radius which is also called the half of the diameters, l is the length of the surface.

Complete step by step answer:
Since from the given question; the radius of the right circular cone is seven centimeters, and the height of the slant is twenty-five centimeters.
Thus, we know the formula for the curved surface of the given cone is $ \pi rl $ .
Substitute the values as $ r = 7,l = 25,\pi = 3.14 $ (pie can be written in the form of irrational number)
Hence, we get $ 2\pi rl = \times (3.14) \times 7 \times 25 $ , solving this value further we get; $ \pi rl = 550c{m^2} $ (centimeter square; because radius and length centimeters also get multiplied).
Thus, the curved surface area of the given cone is $ 550c{m^2} $ .
Now we are going to find the area for the twelve sheets that are required.
Hence multiplied $ 12 $ concerning the area of the surfaced curve, we get $ 12 \times 550 $ .
Further solving the equation, we get $ 12 \times 550 = 6600c{m^2} $ .
Therefore, $ 6600c{m^2} $ is the area of the sheet required for $ 12 $ such caps.

Note: Since the radius is half of the diameter $ r = \dfrac{d}{2} $ because the diameter is the overall measured surface of the given cone and radius is only the right circular surface of the cone; more likely the right-angled triangle of the radius.