Question

The area of the base of a right circular cylinder is $81\pi {\text{c}}{{\text{m}}^2}$ and height of the cylinder is $14{\text{cm}}$. Find its curved surface.

Answer 1

Hint:In this question first write what is given to us it will give us a clear picture of what will be our approach to find the curved surface. Also in order to solve this question we have to use the formula for area of circle and curved surface area of cylinder.

Complete step-by-step solution:

Now it is given that,
The area of the base of a right circular cylinder =$81\pi {\text{c}}{{\text{m}}^2}$
And the height of cylinder =$14{\text{cm}}$.
And we know that,
The area of base of right circular cylinder $ = \pi {r^2}$
Or $\pi {r^2} = 81\pi $
Or ${r^2} = 81$
Or $r = 9{\text{cm}}$
Thus the value of radius of base of the right circular cylinder $ = 9{\text{cm}}$
Now we have to find the value of the curved surface area of the cylinder.
And we know that the curved surface area of the cylinder $ = 2\pi rh$ -----(1)
Now $r = 9{\text{cm, }}h = 14{\text{cm and }}\pi {\text{ = }}\dfrac{{22}}{7}$
Putting the values of r,h and $\pi $ in the equation (1) we get,
Curved surface area$ = 2\pi rh$
$ = 2 \times \dfrac{{22}}{7} \times 9 \times 14$
Or Curved surface area $ = 252 \times \dfrac{{22}}{7}$
Or curved surface area $ = 792{\text{c}}{{\text{m}}^2}$
Thus, the curved surface area of the cylinder $ = 792{\text{c}}{{\text{m}}^2}$.

Note: Whenever we face such types of questions the key concept is that we should write what is given to us. Like we did in this question then we simply apply the formula for the area of the base of the right circular cylinder to find the radius of the base and then we find the curved surface of the area of the cylinder. Thus, we get our desired answer.