Question

The circumference of a circle is 200 feet and height is 12 feet. Find its curved surface area of a cylinder
A) $2400f{{t}^{2}}$
B) $2100f{{t}^{2}}$
C) $2300f{{t}^{2}}$
D) $2010f{{t}^{2}}$

Answer 1

Hint:
Here we have to find the curved surface area of a cylinder. For that, we will first find the radius of the cylinder from the circumference of the circle of the cylinder. From there, we will get the radius of the cylinder. Then we will find the curved surface area of the cylinder using the formula of the curved surface area of the cylinder. Then we will put the values of the radius and height of the cylinder in the formula of curved surface area of the cylinder to get the required answer.

Complete step by step solution:
It is given that the circumference of the circle of the cylinder is 200 feet and the height of the cylinder is 12 feet.
Let the radius of the cylinder be r.
Therefore, the circumference of circle of the cylinder $=2\pi r$
We will put the value of the circumference given in the question.
$200=2\pi r$
We will put the value of pi here.
$200=2\times \dfrac{22}{7}\times r$
On further simplification, we get
$r=\dfrac{350}{11}feet$
Now, we will find the curved surface area of the cylinder
Curved surface area of the cylinder $=2\pi rh$
Now, we will put the value of r, pi and h here.
Curved surface area of the cylinder $=2\times \dfrac{22}{7}\times \dfrac{350}{11}\times 12$
On further simplification, we get
Curved surface area of the cylinder$=2400f{{t}^{2}}$
Therefore, curved surface area of a cylinder is $2400f{{t}^{2}}$

Thus, the correct option is A.

Note:
We need to know the following terms to solve these types of questions:-
1) A cylinder is defined as a three dimensional solid whose top surface and base surface are circular and they are parallel to each other.
2) A curved surface area of a cylinder is defined as the area of only the curved part of the cylinder excluding the top and base circular area.