Praxis Core Academic Skills for Educators: Mathematics (5733)GeometryHard
A manufacturer is designing a new product with a prism-shaped component whose base is a right triangle. The legs of the right triangle are 3 cm and 4 cm, and the height of the prism is 10 cm. What is the volume of this triangular prism?
- A60 cm³
- B150 cm³
- C30 cm³
- D120 cm³
Show answer & explanationAnswer & explanation
Correct answer: A. 60 cm³
The volume of any prism is given by the formula V = Base Area × height. First, calculate the area of the triangular base. For a right triangle, the area is (1/2) × leg1 × leg2. Base Area = (1/2) × 3 cm × 4 cm = (1/2) × 12 cm² = 6 cm². Now, multiply by the height of the prism: V = 6 cm² × 10 cm = 60 cm³.
Why the other options are wrong
- B. Incorrect. This is (3+4)*10 + 3*4, or other miscalculation.
- C. Incorrect. This is (3*10) or (1/2)* (3*4) * (10/2).
- D. Incorrect. This is (3*4)*10, forgetting to divide by 2 for the triangle base area.
Volume of a Triangular Prism
The amount of three-dimensional space occupied by a prism whose bases are triangles.
- Formula: V = B × h, where B is the area of the triangular base and h is the height of the prism.
- Area of triangular base (B) = (1/2) × base_triangle × height_triangle.
- The height of the prism is the perpendicular distance between its two triangular bases.
Memory trick: Base Area first, then 'Stack' it up with height.