Question

a museums tower resembles an inverted cone. the towers diameter is 22 ft, and its height is 15 ft. a contractor will fill the cone with concrete at $5.65 per cubic foot. what is the estimate of the total cost to fill this cone? enter your answer, rounded to the nearest dollar, in the box. use 3.14 for pi. $____

Explanation:

Step1: Calculate the radius of the cone

The diameter $d = 22$ ft, so the radius $r=\frac{d}{2}=\frac{22}{2}=11$ ft.

Step2: Calculate the volume of the cone

The volume formula for a cone is $V=\frac{1}{3}\pi r^{2}h$. Substitute $r = 11$ ft, $h = 15$ ft and $\pi=3.14$. Then $V=\frac{1}{3}\times3.14\times11^{2}\times15$. First, calculate $11^{2}=121$. Then $V=\frac{1}{3}\times3.14\times121\times15$. $\frac{1}{3}\times15 = 5$, so $V=3.14\times121\times5=3.14\times605 = 1899.7$ cubic - feet.

Step3: Calculate the total cost

The cost per cubic - foot is $\$5.65$. So the total cost $C=V\times5.65$. Substitute $V = 1899.7$ into the formula, $C=1899.7\times5.65=1899.7\times(5 + 0.65)=1899.7\times5+1899.7\times0.65=9498.5+1234.805 = 10733.305\approx10733$.

Answer:

$10733$