Question

A trampoline is shaped like a circle. The radius of the trampoline is 5 feet. Around the edge of the trampoline is 0.75 foot wide padded cover over the springs. This pad looks like a ring around the edge of the trampoline.

What is the probability of a student landing on the padded cover over the trampoline springs?

Enter the answer, rounded to the nearest hundredth, in the boxes.

Probability landing on the padded cover over trampoline springs

Answer 1

To find the probability of a student landing on the padded cover over the trampoline springs, we need to compare the area of the padded cover to the area of the entire trampoline.

The area of the entire trampoline is πr^2 = π(5)^2 = 25π square feet.

The inner radius of the padded cover is 5 - 0.75 = 4.25 feet. The outer radius of the padded cover is 5 + 0.75 = 5.75 feet.

The area of the padded cover is π(5.75)^2 - π(4.25)^2 = 57.665 - 56.781 = 0.884 square feet.

Therefore, the answer is 0.884/25π ≈ 0.011 or 1.1%.

Answer 2

Answer: ≅ 0.24

Explanation:

we need to find the area of the padded ring, and the area of the entire circle, and take the ratio of these two.

to find the area of the ring, find the area of the circle include the ring, then the area of the circle without the ring, and subtract them:

.: Area of Ring =
`\pi5.75^2 - \pi5^2`

Area of Ring = 8.0625 pi square ft.

Now, find the area of the entire circle. But wait! we already know this to be 5.75^2 pi square feet!

So we just take the ratio of these to find the probability of landing on the padded cover.

8.0625 pi / 33.0625 pi ≅ 0.24

As a percent, this would be 24%. Basically, we have found the percentage of the entire trampoline covered by the pad.