Question

A diamond is cut in the shape of a triangular pyramid. The triangular base of the pyramid has a base of 4 inches and a height of 5 inches. The height of the pyramid is 6 inches. What is the volume of the diamond? (Recall the formula V = one-third B h.)

Answer 1

Answer:

The volume of diamond is 20 cubic inches.

Step-by-step explanation:

We are given the following in the question:

Triangular base:

Base = 4 inches

Height = 5 inches

Height  of the pyramid = 6 inches

Area of triangular base =

$A = \dfrac{1}{2}\times \text{Base}\times \text{Height}\\\\A = \dfrac{1}{2}\times 4\times 5\\\\A = 10\text{ square inches}$

Volume of diamond = Volume of pyramid

$V=\dfrac{1}{3}\times \text{Area of triangular base}\times \text{Height}\\\\V=\dfrac{1}{3}\times 10\times 6\\\\V = 20\text{ cubic inches}$

Thus, the volume of diamond is 20 cubic inches.