Question

The volume of the triangular pyramid is 110 cubic centimeters. The base of the triangle is 10cm and the height of the triangle is 6cm. Find the height of the pyramid.

Answer 1

height of pyramid is 11 cm

Explanation:

Given:-

- The volume of triangular pyramid, V = 110 cm^3

- The base of triangle, B = 10 cm

- The height of triangle, H = 6 cm

Find:-

Find the height of the pyramid.

Solution:-

- A triangular pyramid is has its base face as a right angle triangle with Base "B" and Height "H". We wil first determine the Base Area of a triangle:

Area = 0.5*B*H

Area = 0.5*10*6

Area = 30 cm^2

- The volume of a pyramid in terms of base area and height "h" of the Pyramid is given as:

Volume = (1/3)*Area*h

- Plug in the values and solve for height of pyramid "h"

h = 3*V / Area

h = 3*110 / 30

h = 11 cm

- The height of the pyramid "h" is 11 cm.

Answer 2

11 centimeters

Explanation:

In this question, we are asked to calculate the height of a triangular pyramid given the volume, the base of the triangle and the height of the triangle

To calculate this, we use the formula below;

Mathematically V = 1/3 AH

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

The area of the triangular base according to the question is 1/2 * b * h = 1/2 * 10 * 6 = 30 square centimeters

Plugging these values we have

110 = 1/3 * 30 * H

110 = 10H

H = 110/10

H = 11 centimeters