Question

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

Answer 1

Hint: We are given the circumference of a circle and height. The equation for calculating the curved surface area is given by ${2 \times \pi \times \text{r} \times \text{h}}$. So the curved surface area can be calculated by substituting the values of the circumference of the circle and the height, as the surface area of the cylinder is equal to the product of circumference of the circle and its height.

Complete step by step solution: We can draw the figure of the cylinder with height h and the curved surface of the cylinder cut open along its height.

We are provided with the circumference and height.
The circumference is given by, ${2\pi \text{r} = 200 \text{ft}}$
The height is given by \[{\text{h} = 12\text{ft}}\]
The equation for curved surface area is given by, ${2 \times \pi \times \text{r} \times \text{h}}$. This can be written as a product of circumference of circle and height. So, the curved surface area is given by,
Curved surface area $=2\pi \text{rh} \Rightarrow 200 \times 12 = 2400 \text{ft}^{2} $
Hence the required curved surface area of the cylinder is $2400 \text{ft}^{2}$

Therefore, the correct answer is option A.

Note: We can also solve this problem in the following way. The circumference is given. From that, we can find the radius using the relation ${\text{c} = 2\pi \text{r}}$. The height is also given. So, we can find the curved surface area using the equation C.S.A ${ = 2 \times \pi \times \text{r} \times \text{h}}$. This method is a bit longer than the other method. We must write the units and do necessary unit conversions while doing problems of this type.