The lateral surface area of a cone is: S = πrl

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.

Source: Vesuvius from plane, Pastorious, Wikipedia

Looking at the crater as a cone as shown below, how many acres of land cover the surface of the interior of Vesuvius’ huge crater? (One acre is equal to 43,560 square feet.)

First, draw and label a figure. Drag the dimensions from below onto the appropriate place in the figure.

• The problem is asking us to find the __?__ of the cone that represents the Gran Cono crater of Mount Vesuvius.
  
  Interactive popup. Assistance may be required. Check Your Answer lateral surface area
  
  
• The formula for lateral surface area of a cone is ___?____.
  
  Interactive popup. Assistance may be required. Check Your Answer S = πrl
  
  
• The radius is ____?_____.
  
  Interactive popup. Assistance may be required. Check Your Answer 350 feet

The slant height, l, is missing.

• In order to find the slant height, l, we will need to use the Pythagorean Theorem.
  
  
• What are the values of the legs of the right triangle?
  
  Interactive popup. Assistance may be required. Check Your Answer 200 ft and 350 ft
  
  
• Find the slant height, l.
  
  Interactive popup. Assistance may be required. Check Your Answer l² = 200² + 350²
  l² = 40,000 + 122,500
  l² = 162,500
  l = √162,500
  l ≈ 403 ft
  
  
• Use the formula to find the lateral surface area of the cone, the lateral area of the cone-shaped crater.
  
  Interactive popup. Assistance may be required. Check Your Answer S = πrl = π(350 ft)(403 ft) = 443,122 ft²
  

The answer is in square feet, find the area in acres.

• If one acre is 43,560 ft², then the cone-shaped crater has a lateral area of _?_ acres.
  
  Interactive popup. Assistance may be required. Check Your Answer 443,122 ÷ 43,560 ≈ 10.17