Question

Find the volume of a right circular cone that has a height of 18.9 in and a base with a circumference of 15 in. Round your answer to the nearest tenth of a cubic inch.

Answer 1

112.8

Explanation:

Answer 2

The volume of the cone is:

• 112.6 cubic inches.

Explanation:

You should know that the volume of a straight circular cone is equal to:

• Cone volume = (1/3) PI * r ^ 2 * h

Where:

r = radius.

h = height.

Since the radius and diameter are not provided in the exercise but the circumference, the circumference formula should be used and the diameter must be cleared:

• 
  `\bold{Circumference} = \bold{PI * Diameter}.`

When clearing you get:

• 
  `\bold{Diameter} = \bold{circumference / PI}`

By replacing the data you get:

• 
  `\bold{Diameter = 15 \ inches / PI}`
• 
  `\bold{Diameter = 4.77 \ inches}.`

Since the radius is equal to half the diameter, then the diameter is equal to 2,385 inches, now having the value of radius we proceed to replace in the volume formula:

• 
  `\bold{Cone \ volume = (1/3) PI * 2.385 in^2 * 18.9 in}`
• 
  `\bold{Cone \ volume = 112.581541 \ in^3}`
• 
  `\bold{Cone \ volume = 112.6 \ in^3}`