Question

The volume of a triangular pyramid is 110 cm³. The base of the triangle is 10 cm in the height of the triangle is 6 cm. Find the height of the pyramid.

Answer 1

Answer:

The height of the pyramid is 11 cm.

Step-by-step explanation:

We are given the following in the question:

Volume of triangular pyramid = 110 cubic cm

Base of trianle,b = 10 cm

Height of triangle,h = 6 cm

Area of triangular base =

$A = \dfrac{1}{2}\times b\times h\\\\A = \dfrac{1}{2}\times 10\times 6\\\\A = 30\text{ square cm}$

Volume of triangular pyramid =

$V = \dfrac{1}{3}AH$

where H is the height of the pyramid, A is the area of triangular base.

Putting values, we get,

$110 = \dfrac{1}{3}\times 30\times H\\\\H = \dfrac{3\times 110}{30}\\\\H = 11\text{ cm}$

Thus, height of the pyramid is 11 cm.