Question

A ball pit is in the shape of a cylinder with a lateral surface area of 245 square feet. The diameter of the ball pit is 312 inches. What is the height of the ball pit to the nearest foot?

Answer 1

Answer:

Height of the ball pit is nearly 3 ft.

Step-by-step explanation:

Given:

diameter of ball pit = 312 inches

But radius is half of the diameter.

Hence radius r = $\frac{diameter}{2} = \frac{312}{2} = 156 \ in.$

Lateral Surface area of cylinder = 245 sq ft.

We need to find the height of cylinder.

Now lateral surface area is in feet and radius is in inches, we will first convert the radius which is inches to feet we get;

12 inches = 1 feet

hence 156 inches  =  feet in 156 inches

We will use Unitary method to find the same;

feet in 156 inches = $\frac{156}{12} =13 ft.$

Hence radius of ball pit = 13 ft.

Now Lateral surface area of cylinder is given by:

Lateral surface area of cylinder= $2\pi rh$

Substituting the given values in above formula we get;

$2\times\pi\times 13\times h=245\\ 81.64h=245\\\\h=\frac{245}{81.64} \approx 3 \ ft$

Hence height of the ball pit is nearly 3 ft.