Question

The base of a pyramid is a triangle whose base is 3 ft and whose height is 8 ft. If the pyramid
is 9 ft high, what is its volume?
(a) 56 ft
(b) 108ft
(c) 72 ft
(d) 36 ft​

Answer 1

Answer:

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Answer 2

Answer:

The correct answer is option(d)

Step-by-step explanation:

Given,

The base of triangular base of the pyramid = 3ft

Height of the triangular base of the pyramid = 8ft

Height of the pyramid = 9ft

To find,

The volume of the pyramid

Recall the concept

Volume of a pyramid = $\frac{1}{3}$ × base area × height

Volume of triangle =$\frac{1}{2}$ × base × height

Solution:

Since the base of the pyramid is triangular shape,

Base area = area of the triangle

Since the base of the triangle is 3ft and the height of the triangle is 8ft

Area of the triangle = $\frac{1}{2}$ × base × height

= $\frac{1}{2}$ ×3 ×8

= 12square ft.

The base area of the pyramid = 12square ft.

The volume of the pyramid =   $\frac{1}{3}$ × base area × height

Since the height of the pyramid = 9ft

Volume of the pyramid =  $\frac{1}{3}$ × 12 × 9

= 36 cubic ft

The volume of the pyramid = 36 cubic ft

The correct answer is option(d)

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