Question

1. what dimensions would you need to measure the volume of the following prism? image of a triangular prism

• radius of the rectangle, length of the rectangle, width of the triangle
• base of the triangle, height of the triangle, height of the prism
• hypotenuse of the triangle, height of the prism, width of the triangle
• height of the prism, radius of the triangle, height of the triangle

Explanation:

Step1: Recall Volume Formula for Triangular Prism

The volume \( V \) of a triangular prism is given by the formula \( V = \text{Area of triangular base} \times \text{height of the prism} \). The area of a triangle is \( \frac{1}{2} \times \text{base of triangle} \times \text{height of triangle} \). So, we need the base and height of the triangular base, and the height (length) of the prism.

Step2: Analyze Each Option

• Option 1: "radius of the rectangle, length of the rectangle, width of the triangle" – Rectangles don't have radii, and this mixes incorrect terms. Eliminate.
• Option 2: "base of the triangle, height of the triangle, height of the prism" – Matches the formula: base and height of triangle (for area of base) and height of prism (length of prism). This is correct.
• Option 3: "hypotenuse of the triangle, height of the prism, width of the triangle" – Hypotenuse isn't needed for area of triangle (we use base and height). Eliminate.
• Option 4: "height of the prism, radius of the triangle, height of the triangle" – Triangles don't have radii. Eliminate.

Answer:

B. base of the triangle, height of the triangle, height of the prism