Question

A family is building a circular fountain in the backyard. The yard is rectangular and measures 10x by 15x and the fountain is going to be circular with a radius of 4x. Once the fountain is build, what will be the area of the remaining yard?

Answer 1

yard-fountain

yard=rectangle=lenght times width=10x times 15x=150x²

area fountain=circle=pir²=pi(4x)²=16x²pi

yard-fountain=150x²-16x²pi≈137.43x² square yards

Answer 2

Area of the rectangle(A) is given by:

`A = lw`

where,

l is the length and w is the width of the rectangle respectively.

As per the statement:

The yard is rectangular and measures 10x by 15x

⇒
`\text{Area of rectangular yard}=10x \cdot 15x = 150x^2`

It is also given that:

the fountain is going to be circular with a radius of 4x.

Area of a circle(A') is given by:

`A' = \pi r^2` where, r is the radius of the circle.

Use
`\pi = 3.14`

then;

`\text{Area of a circular fountain} = \pi (4x)^2 = 16x^2 \cdot 3.14 = 50.24x^2`

We have to find the he area of the remaining yard.

`\text{Area of the remaining yard} = \text{Area of the rectangular yard} - \text{Area of a circular fountain}`

Substitute the given values we have;

`\text{Area of the remaining yard} = 150 x^2-50.24x^2 = 99.76 x^2`

Therefore, the area of the remaining yard will be,
`99.76 x^2`