Questions: Q. A large conical mound of sand with a diameter of 45 feet and height of 15 feet is being stored as a key raw ingredient for products at your glass manufacturing company. What is the approximate volume of the mound?

Solution Steps

To find the volume of a conical mound, we use the formula for the volume of a cone: \( V = \frac{1}{3} \pi r^2 h \), where \( r \) is the radius of the base and \( h \) is the height. First, calculate the radius by dividing the diameter by 2. Then, substitute the radius and height into the formula to compute the volume.

The diameter of the conical mound is given as 45 feet. To find the radius, we divide the diameter by 2:

\[ r = \frac{45}{2} = 22.5 \text{ feet} \]

The formula for the volume of a cone is:

\[ V = \frac{1}{3} \pi r^2 h \]

where \( r \) is the radius and \( h \) is the height. Substituting the known values:

\[ V = \frac{1}{3} \pi (22.5)^2 (15) \]

Perform the calculations:

\[ V = \frac{1}{3} \pi \times 506.25 \times 15 \]

\[ V = \frac{1}{3} \times 2384.8125 \times 15 \]

\[ V = 7952.1564 \text{ cubic feet} \]

Final Answer