A family is having a pool built in their backyard. If their yard is rectangular and measures 7x by 6x and the pool is circular with a radius of 2x how much of the yard will be left over after the pool is built?
(7*6) - 2^2π = ?
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.
Step 1: Calculate the area of the rectangular yard.
The area of a rectangle is calculated by multiplying its length by its width. In this case, the length of the yard is 7x and the width is 6x. So, the area of the yard is (7x) * (6x) = 42x^2.
Step 2: Calculate the area of the circular pool.
The area of a circle is calculated by multiplying the square of its radius by Pi (π). In this case, the radius of the pool is 2x. So, the area of the pool is π * (2x)^2 = 4πx^2.
Step 3: Subtract the area of the pool from the area of the yard.
To find the remaining area of the yard, we subtract the area of the pool from the area of the yard. The remaining area is 42x^2 - 4πx^2.
So, the expression for the remaining area of the yard after the pool is built is 42x^2 - 4πx^2.
To find out how much of the yard will be left over after the pool is built, we first need to calculate the area of the pool. Then, we subtract this area from the total area of the yard.
1. Calculate the area of the pool:
- The radius of the pool is given as 2x.
- The formula to calculate the area of a circle is: A = π * r^2, where A is the area and r is the radius.
- Plugging in the radius, we get: A = π * (2x)^2 = π * 4x^2.
2. Calculate the total area of the yard:
- The dimensions of the yard are given as 7x by 6x.
- The formula to calculate the area of a rectangle is: A = length * width.
- Plugging in the dimensions of the yard, we get: A = (7x) * (6x) = 42x^2.
3. Subtract the area of the pool from the total yard area:
- Total yard area - Pool area = 42x^2 - π * 4x^2 = x^2 (42 - 4π).
Therefore, after the pool is built, there will be x^2 (42 - 4π) square units of the yard left over.