Praxis Core Academic Skills for Educators: Mathematics (5733)GeometryHard
A sculptor is creating a large pyramid structure for an exhibit. The pyramid has a square base with sides of 10 feet and a height of 12 feet. The sculptor needs to calculate the volume of the pyramid to determine the amount of material required. What is the volume of the pyramid?
- A200 cubic feet
- B120 cubic feet
- C1200 cubic feet
- D400 cubic feet
Show answer & explanationAnswer & explanation
Correct answer: D. 400 cubic feet
The volume of a pyramid is given by the formula V = (1/3) × A_base × h, where A_base is the area of the base and h is the height. For a square base, A_base = side². Substitute the given values (side=10ft, h=12ft) into the formula.
Why the other options are wrong
- A. This is incorrect; it might be a result of squaring the height or using an incorrect base area.
- B. This is incorrect; it might be a result of using the side length as the base area or an incorrect fraction.
- C. This is incorrect; it is the volume of a prism with the same base and height, not a pyramid (which is 1/3 of a prism).
Volume of a Pyramid
The amount of three-dimensional space occupied by a pyramid, calculated as one-third the product of its base area and height.
- Formula: V = (1/3) × A_base × h.
- A_base depends on the shape of the base (e.g., square, triangle).
- The height (h) is the perpendicular distance from the apex to the base.
Memory trick: Pyramid volume: 'Base Area' times 'Height', then 'Divide by 3'!