Question

Christy and Emily both have circular pools in their backyard. The surface area of Christy’s pool is 16 times greater than that of Emily’s pool.



How much greater is the diameter of the larger pool?


4 times


16 times


32 times


8 times

Answer 1

The diameter of Christy's pool is 4 times larger than the other .-.

How to find the relation between the radius of each pool?

We know that for a circle of radius R the area is given by:

A = π*R^2

Let's say that:

• R is the radius of Christy's pool
• R' is the radius of Emily's pool.

Then we have the corresponding areas.

• A = π*R^2
• A' = π*R'^2

We know that:

A = 16*A'

Replacing the equations, we get:

π*R^2 = 16*(π*R'^2)

R^2 = 16*R'^2

If we apply the square root in both sides, we get:

√R^2 = √(16*R'^2)

R = 4*R'

This means that the radius of Christy's pool is 4 times larger than the one of Emily's pool.

And the same is for the diameter (twice the radius).

D = 2*R

D' = 2*R'

Then:

D = 2*R = 2*(4*R') = 4*(2*R') = 4*D'

The diameter of Christy's pool is 4 times larger than the other diameter.

If you want to learn more about circles, you can read:

https://brainly.com/question/25306774