The famous rotunda of the Capital Bldg has a floor that is 96 feet in diameter. A marble restoration company charges $40 per sq. yard for its services. How much would it cost to restore the entire floor in the rotunda?
My answer 96 feet in diameter C=πd
96+3.14π=105.9
No
They are chargint $40 per <b<square yard, so we are dealing with area, not circumference
Area = πr^2
= π(48)^2
= 2304π feet ^2
= 256π yards^2
cost = $40(256π)
= $32,169.91
or appr $32,170
Your answer of only $105.90 should have sounded totally unreasonable to you .
To calculate the cost of restoring the entire floor in the rotunda, we first need to determine the area of the floor.
The formula for the area of a circle is A = πr^2 (where A is the area and r is the radius). Since we have the diameter (96 feet), we can divide it by 2 to get the radius, which is 48 feet.
Plugging the values into the formula:
A = π(48)^2
A = 3.14 * 48 * 48
A = 7234.56 square feet
To convert square feet to square yards, we need to divide the area by 9 since 1 yard is equal to 3 feet.
Area in square yards = 7234.56 / 9
Area in square yards = 803.84 square yards
Now, we multiply the area in square yards by the cost per square yard, which is $40.
Cost to restore the entire floor = 803.84 * 40
Cost to restore the entire floor = $32,153.60
Therefore, it would cost approximately $32,153.60 to restore the entire floor in the rotunda.