A family is having a pool built in their backyard. If their backyard is rectangular and measures 8x by 7x and the pool is circular with a radius of 3x how much of the yard will be left over after the pool is built?

Question

A family is having a pool built in their backyard. If their backyard is rectangular and measures 8x by 7x and the pool is circular with a radius of 3x how much of the yard will be left over after the pool is built?

a. 56𝑥^2−9𝜋𝑥^2
b. 65𝑥^2
c. 56𝑥^2−3𝜋𝑥^2
d. 65𝜋𝑥^2

Answer 1

8x * 7x = 56x^2 = whole yard

𝜋 (3x)^2 = 𝜋 9 x^2 = pool
left over yard = whole yard - pool = 56x^2 - 9𝜋 x^2

Answer 2

Well, it seems like we've got a backyard showdown between a rectangle and a circle! Let's see who wins.

The area of the rectangular backyard is 8x by 7x, which gives us a total area of (8x)*(7x) = 56x^2.

Now, the pool is circular with a radius of 3x. To find the area of a circle, we use the formula A = πr^2, where A is the area and r is the radius.

Plugging in the radius of 3x, we get A = π*(3x)^2 = 9πx^2.

To find the leftover area after the pool is built, we simply subtract the area of the pool from the total area of the backyard: 56x^2 - 9πx^2.

So, the correct answer is option a) 56x^2 - 9πx^2.

Remember, even if the backyard loses a bit of space to the pool, you can always make it up by doing some synchronized swimming or hosting pool parties!

Answer 3

To find out how much of the yard will be left over after the pool is built, we need to calculate the area of the yard and subtract the area of the pool.

The area of a rectangle is found by multiplying its length by its width.

The area of the yard is given as 8x by 7x, so the area of the yard is (8x) * (7x) = 56x^2.

The area of a circle is found by multiplying pi (π) by the square of its radius.

The radius of the pool is given as 3x, so the area of the pool is π * (3x)^2 = 9πx^2.

Subtracting the area of the pool from the area of the yard, we get 56x^2 - 9πx^2.

Therefore, the answer is option a. 56𝑥^2−9𝜋𝑥^2.

Answer 4

To find out how much of the yard will be left over after the pool is built, we need to calculate the area of the rectangular yard and subtract the area of the circular pool.

The area of a rectangle is given by the formula: Area = length × width.

In this case, the length of the yard is 8x and the width is 7x, so the area of the yard is (8x) × (7x) = 56x^2.

The area of a circle is given by the formula: Area = π × radius^2.

In this case, the radius of the circular pool is 3x, so the area of the pool is π × (3x)^2 = 9πx^2.

Now, to find the area of the yard left over, we subtract the area of the pool from the area of the yard:

Area left over = Area of yard - Area of pool
= 56x^2 - 9πx^2

So, the correct option is:

a. 56x^2 - 9πx^2