You are standing next to a really big circular lake. You want to measure the diameter of the lake, but you don't want to have to swim across with a measuring tape! You decide to walk around the perimeter of the lake and measure its circumference, and find that it's [tex]$400 \pi m$[/tex]. What is the diameter [tex]$d$[/tex] of the lake?
[tex]d=\square m$[/tex]

Question

You are standing next to a really big circular lake. You want to measure the diameter of the lake, but you don't want to have to swim across with a measuring tape! You decide to walk around the perimeter of the lake and measure its circumference, and find that it's [tex]$400 \pi m$[/tex]. What is the diameter [tex]$d$[/tex] of the lake? 
[tex]d=\square m$[/tex]

GinnyAnswer · Answer

Recall the formula for the circumference of a circle: C = π d . 
 Substitute the given circumference: 400 π = π d . 
 Divide both sides by π to solve for d . 
 The diameter of the lake is: $\boxed{400} m. 
 
 Explanation 
 
 Problem Analysis We are given a circular lake and its circumference, and we need to find the diameter of the lake. 
 
 Recall the circumference formula The formula for the circumference C of a circle with diameter d is given by: C = π d 
 
 Substitute the given circumference We are given that the circumference C of the lake is 400 π meters. Substituting this value into the formula, we get: 400 π = π d 
 
 Solve for the diameter To find the diameter d , we need to isolate d by dividing both sides of the equation by π :
 π 400 π ​ = π π d ​ d = 400 
 
 State the final answer Therefore, the diameter of the lake is 400 meters.

Examples 
 Imagine you're designing a circular park and want to build a fence around it. If you know the length of the fence (the circumference), you can easily calculate the distance across the park at its widest point (the diameter) using the formula C = π d . This helps in planning the layout and features of the park effectively.

Answer (1)

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