Question

Find the volume of the following. Please round your answer to the nearest tenth. Please do not put units.

Answer 1

Answer:

The volume of the given figure is 150 mm³

Step-by-step explanation:

The formula of the volume of the triangular pyramid is V = $\frac{1}{3}$ AH, where

• A is the area of its base

• H is its height

The formula of the area of a triangle is A = $\frac{1}{2}$ bh, where

• b is the length of its base

• h is the length of its height

In the given figure

∵ The pyramid has a triangular base

∵ The triangle has a base of 12 mm and a height of 7.5 mm

∴ b = 12 mm and h = 7.5 mm

→ By using the 2nd formula above, find the area of the base

∴ A = $\frac{1}{2}$ (12)(7.5)

∴ A = 45 mm²

∵ The height of the pyramid is 10 mm

∴ H = 10 mm

∵ A = 45 mm²

→ Substitute them in the first formula above to find the volume

∴ V = $\frac{1}{3}$ (45)(10)

∴ V = 150 mm³

∴ The volume of the given figure is 150 mm³