Question

A state capital building has a circular floor 94 feet in diameter. The legislature wishes to have the floor carpeted. The lowest bid is $78 per square yard, including installation.

What is the area of the circular floor in square feet? (Round your answer to two decimal places.)

ft2
What is the area of the circular floor in square yards? (Round your answer to two decimal places.)
yd2
How much must the legislature spend (in dollars) for the carpeting project? Round to the nearest dollar.
$

Answer 1

The area of the circular floor in square feet is 6,939.78 ft².

The area of the circular floor in square yards is 771.09 yd².

The legislature must spend $60,145 for the carpeting project.

Explanation:

The area of a circle is given by the formula A = πr², where r is the radius of the circle. The radius of a circle is half its diameter.

Given the diameter of the state capital building's circular floor is 94 feet, its radius is:

`\implies r=(94)/(2)=47\sf \;ft`

To find the area of the circular floor in square feet, substitute r = 47 into the formula for area of a circle:

`\begin{aligned}\implies \sf Area &= \pi(47)^2\\&=2209\pi\\&=6939.78\;\sf ft^2\;(2\;d.p.)\end{aligned}`

Therefore, the area of the circular floor in square feet is 6,939.78 ft² (rounded to two decimal places).

To convert square feet to square yards, divide the area in square feet by 9. Therefore, the area of the circular floor in square yards is:

`\begin{aligned}\implies \sf Area &= (2209\pi)/(9)\\&=771.09\; \sf yd^2\;(2\;d.p.)\end{aligned}`

Therefore, the area of the circular floor in square yards is 771.09 yd² (rounded to two decimal places).

To find the total cost of the project, given the lowest bid for the project is $78 per square yard, multiply the area of the circular floor in square yards by the cost per square yard:

`\begin{aligned}\implies \sf Total\;cost &=771.09 \cdot \$78\\&=\$60145.02\end{aligned}`

Therefore, the legislature must spend $60,145 for the carpeting project, (rounded to the nearest dollar).