The base of a right prism is a right triangle. The lengths of the legs of the triangle are 3 meters and 5 meters. The volume of the prism is 30 cubic meters. Find the height of the prism. A. 2 m B. 4 m C. 6 m D. 10 m

The height = 4 m answer (B)

Step-by-step explanation:

∵ The volume of any prism = base area * height

∵ The base is a right angle Δ with 3 and 5

∴ Area the base = 1/2 * 3 * 5 = 7.5 m²

∵ the volume of it = 30 m³

∴ 30 = 7.5 * height

∴ The height = 30 : 7.5 = 4 m

B. 4 m

Step-by-step explanation:

The volume of a right prism is given by

V = Bh

Where B is the area of the base and h is the height

B = 1/2 bh where b is 3 and h = 5

B = 1/2 (3) (5)

= 7.5

V = Bh

30 = 7.5 * h

Divide by 7.5 on each side

30/7.5 = 7.5 / 7.5 h

4 = h

The height is 4 m