Praxis Core Academic Skills for Educators: Mathematics (5733)GeometryMedium
A sculptor is creating a cone-shaped artwork. The cone has a radius of 3 feet and a height of 7 feet. What is the approximate volume of the cone?
- A147 π cubic feet
- B21 π cubic feet
- C63 π cubic feet
- D42 π cubic feet
Show answer & explanationAnswer & explanation
Correct answer: B. 21 π cubic feet
The volume of a cone is given by the formula V = (1/3) * π * r² * h. Given a radius (r) of 3 feet and a height (h) of 7 feet: V = (1/3) * π * (3)² * 7 = (1/3) * π * 9 * 7 = π * 3 * 7 = 21π cubic feet.
Why the other options are wrong
- A. This is pi * radius * height^2, an incorrect formula.
- C. This is pi * radius^2 * height, forgetting to multiply by 1/3.
- D. This is radius * height * 2 * pi, or 2 * (1/3) * pi * r^2 * h.
Volume of a Cone
The amount of three-dimensional space occupied by a cone.
- Formula: V = (1/3) * π * r² * h, where r is the radius and h is the height.
- The height must be perpendicular to the base.
- Units are cubic units (e.g., cubic feet, cubic meters).
Memory trick: Base area times height, then for pointy shapes, a third is just right!