Example: In the year 79 A.D., Mount Vesuvius in Italy erupted so suddenly that it buried the city of Pompeii and most of its residents. Volcanologists have compared the dimensions of the crater formed by this eruption with other volcano craters throughout the world. Mount Vesuvius’ cone-shaped crater, called Gran Cono, has a diameter of 700 feet and is 200 feet deep. If the crater were to fill with magma again, how many dump truck loads of magma would be in Vesuvius’ huge crater? (The average dump truck load is considered to be 18 cubic yards.)

First, Draw and Label a Figure

Drag the dimensions to the appropriate place on the figure.

Use the diagram to answer the following questions. Click the blanks to reveal the answers.

• To find the number of dump trucks needed to fill the crater with magma, the first step is to find the Interactive popup. Assistance may be required. __________ volume of the crater.
• The crater is in the shape of a cone. The formula for the volume of a cone is Interactive popup. Assistance may be required. __________ V = 1 3 πr²h or V = 1 3 Bh .
• The radius of the cone is Interactive popup. Assistance may be required. __________ 350 feet .
• The height of the cone is Interactive popup. Assistance may be required. __________ 200 feet .
• The volume of the cone is Interactive popup. Assistance may be required. __________ V = 1 3 π(350 ft)²(200 ft) = 1 3 π(122,500 ft²)(200 ft) ≈ 8,1666,666.67π ft³ ≈ 25,656,340 ft³ .
• A dump truck holds Interactive popup. Assistance may be required. __________ 18 cubic yards.
• The dump truck holds cubic yards and our answer is in cubic feet. Since a cubic yard is 3 feet on each side, to change from cubic feet to cubic yards, divide the volume by Interactive popup. Assistance may be required. __________ 3 ft 1 yd X 3 ft 1 yd X 3 ft 1 yd = 27 ft³ yd³ to change cubic feet to cubic yards.
• The volume of the cone in cubic yards is Interactive popup. Assistance may be required. __________ V = 25,656,340 ft³ ÷ 27 ft³ yd³ ≈ 950,234.8 yd³ .
• If the average dump truck carries 18 cubic yards, then it would take Interactive popup. Assistance may be required. __________ 950,234.8 yd³ ÷ 18 ≈ 52,791 full dump truck loads to fill the Gran Cono crater of Mount Vesuvius with magma.

Watch this video summarizing the formula of the volume of a cone.