Question

A circular pool with a 10-foot diameter is surrounded by a deck.

A square with side lengths of 15 feet. A circle with a 10 foot diameter is in the center.

What is the area of the deck that surrounds the pool? Use 3.14 for Pi.
146.5
193.6
225.0
303.5

Answer 1

The area of the deck that surrounds the pool can be found by subtracting the area of the circular pool from the area of the square deck.

The area of the circular pool is:

A = πr^2

A = π(5)^2

A = 78.5 square feet

The area of the square deck is:

A = s^2

A = (15)^2

A = 225 square feet

Therefore, the area of the deck that surrounds the pool is:

A = 225 - 78.5

A = 146.5 square feet

Therefore, the correct answer is: 146.5.

Answer 2

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The area of the circular pool,
`\displaystyle\sf A_{\text{pool}}`, can be calculated using the formula
`\displaystyle\sf A_{\text{pool}}=\pi r^(2)`, where
`\displaystyle\sf r` is the radius of the pool. Since the diameter of the pool is 10 feet, the radius is half of that, which is 5 feet. Therefore, the area of the pool is:

`\displaystyle\sf A_{\text{pool}}=\pi (5)^(2)`

The area of the square,
`\displaystyle\sf A_{\text{square}}`, can be calculated using the formula
`\displaystyle\sf A_{\text{square}}=s^(2)`, where
`\displaystyle\sf s` is the side length of the square. In this case, the side length is 15 feet. Therefore, the area of the square is:

`\displaystyle\sf A_{\text{square}}=(15)^(2)`

To find the area of the deck,
`\displaystyle\sf A_{\text{deck}}`, we subtract the area of the pool from the area of the square:

`\displaystyle\sf A_{\text{deck}}=A_{\text{square}}-A_{\text{pool}}`

Substituting the calculated values:

`\displaystyle\sf A_{\text{deck}}=(15)^(2)-\pi (5)^(2)`

Simplifying:

`\displaystyle\sf A_{\text{deck}}=225-\pi (25)`

Using
`\displaystyle\sf \pi =3.14`:

`\displaystyle\sf A_{\text{deck}}=225-3.14* 25`

Finally, evaluating the expression:

`\displaystyle\sf A_{\text{deck}}=225-78.5=146.5`

Therefore, the area of the deck that surrounds the pool is 146.5 square feet.

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