Question

An ice rink is 200 feet long and 85 feet wide. The four corners of the rink are rounded to a radius of 24 feet. What is the surface area of the rink? Round the answer to the nearest square foot.

Answer 1

Each rounded corner is a quarter of a circle with a radius of 24 feet, so the area of each corner is 1/4 * π * (24)^2 = 144π square feet. The surface area of the ice rink is 17,000 + 576π square feet.

Step-by-step explanation:

To find the surface area of the ice rink, we need to determine the areas of the rectangular part of the rink and the four rounded corners.

The rectangular part has a length of 200 feet and a width of 85 feet, so its area is 200 * 85 = 17,000 square feet.

Each rounded corner is a quarter of a circle with a radius of 24 feet, so the area of each corner is 1/4 * π * (24)^2 = 144π square feet.

Multiply this by 4, since there are four corners, to get a total corner area of 576π square feet.

Adding the rectangular area and the corner area, the surface area of the ice rink is 17,000 + 576π square feet.

Answer 2

The surface area of the ice rink is equal to
`15190.44ft^(2)`

Why?

To calculate the area of the ice rink, we need to remember that the surface area of the four coners (with radius of 24 feet) is equal to the area of a single circle with a radius of 24 feet.

So, calculating the area we have:

`SurfaceArea=TotalArea-CircleArea\\\\SurfaceArea=200ft*85ft-\pi *radius^(2)\\\\SurfaceArea=17000ft^(2)-\pi *(24ft)^(2)=17000ft^(2)-1809.56ft^(2)=15190.44ft^(2)`

Hence, we have that the surface area of the ice rink is equal to
`15190.44ft^(2)`

Have a nice day!