Question

Harry measures the big prize wheel on a game show and calculates that it has an area of 12.56 square yards. What is the prize wheel diameter?

Answer 1

To find the diameter of the prize wheel, use the formula A = πr². Plug in the given area and solve for the radius. The diameter is twice the radius.

Step-by-step explanation:

To find the prize wheel diameter, we need to know the formula for finding the area of a circle, which is A = πr². We are given that the area of the prize wheel is 12.56 square yards. Let's plug this value into the formula and solve for the radius:

12.56 = πr²

To isolate r², divide both sides of the equation by π:

12.56 ÷ π = r²

Now, take the square root of both sides to find r:

√(12.56 ÷ π) = r

Using a calculator, we can approximate this value to be r ≈ 2.00 yards.

The diameter of the prize wheel is simply twice the radius, so the diameter is approximately 4.00 yards.

Answer 2

The prize wheel diameter is 4.00 yards

Step-by-step explanation:

Area (A) = πd^2/4

πd^2 = 4A

d^2 = 4A/π

d (diameter) = √(4A/π)

A = 12.56 square yards, π = 3.142

d = √(4×12.56/3.142) = √15.99 = 4.00 yards