Question

1. an architect is making a plan for a new circular playground. if the picture below is the playground, how much fencing needs to go up to keep the kids in the circle? 2) the circumference of a circle maze is 36.31 meters. how many meters is it to the middle of the maze? 3) the radius of a birthday cake is 5 inches. icing will decorate the circumference of the cake. what is the circumference? 4) the radius of a truck tire is 11 inches. what is the diameter of the tire? 5) mr. lewis designed a circular walkway in front of his house. the circumference of the walkway is 18.84 feet. how many meters is the walkway if you crossed through the middle? ex: a bicycle trail in the shape of a circle has a diameter of 3 miles. michelle biked around the trail 4 times. about how far did michelle bike?

Explanation:

Problem 1

Step1: Identify the formula for circumference

The formula for the circumference of a circle is \( C = \pi d \), where \( d \) is the diameter. Here, the diameter \( d = 64 \) m.

Step2: Calculate the circumference

Substitute \( d = 64 \) into the formula: \( C=\pi\times64\approx3.14\times64 = 200.96 \) m.

Step1: Recall the formula for circumference

The formula for the circumference of a circle is \( C = 2\pi r \) (or \( C=\pi d \), and \( r=\frac{d}{2} \)). We need to find the radius \( r \) (distance to the middle), so we can use \( C = 2\pi r \) and solve for \( r \): \( r=\frac{C}{2\pi} \).

Step2: Substitute the given circumference

Given \( C = 36.31 \) meters, substitute into the formula: \( r=\frac{36.31}{2\times3.14}\approx\frac{36.31}{6.28}\approx5.78 \) meters.

Step1: Recall the formula for circumference

The formula for the circumference of a circle is \( C = 2\pi r \), where \( r \) is the radius. Here, \( r = 5 \) inches.

Step2: Calculate the circumference

Substitute \( r = 5 \) into the formula: \( C = 2\times3.14\times5= 31.4 \) inches.

Answer:

200.96 meters

Problem 2