Sample Problems on Volume of a Pyramid

Problem 1: What is the volume of a square pyramid if the sides of a base are 6 cm each and the height of the pyramid is 10 cm?

Solution:

Given

• Length of Side of Base of Square Pyramid = 6 cm
• Height of Pyramid = 10 cm

Volume of Square Pyramid (V) = 1/3 × Area of square base × Height

Area of square base = a² = 6² = 36 cm²

V = 1/3 × (36) ×10 = 120 cm³

Hence, volume of the given square pyramid is 120 cm³.

Problem 2: What is the volume of a triangular pyramid whose base area and height are 120 cm²  and 13 cm, respectively?

Solution:

Given

• Area of Triangular Base = 120 cm²
• Height of Pyramid = 13 cm

Volume of a Triangular Pyramid (V) = 1/3 × Area of Triangular Base × Height

V = 1/3 × 120 × 13 = 520 cm³

Hence, volume of the given triangular pyramid = is 520 cm³

Problem 3: What is the volume of a triangular pyramid if the length of the base and altitude of the triangular base are 3 cm and 4.5 cm, respectively, and the height of the pyramid is 8 cm?

Solution:

Given

• Height of Pyramid = 8 cm
• Length of Base of Triangular Base = 3 cm
• Length of Altitude of Triangular Base = 4.5 cm

Area of Triangular Base (A) = 1/2 b × h = 1/2 × 3 × 4.5 = 6.75‬ cm²

Volume of Triangular Pyramid (V) = 1/3 × A × H

V = 1/3 × 6.75 × 8 = 18 cm³

Hence, volume of the given triangular pyramid is 18 cm³

Problem 4: What is the volume of a rectangular pyramid if the length and width of the rectangular base are 8 cm and 5 cm, respectively, and the height of the pyramid is 14 cm?

Solution:

Given

• Height of Pyramid = 14 cm
• Length of Rectangular Base (l) = 8 cm
• Width of Rectangular Base (w) = 5 cm

Area of Rectangular Base (A) = l‬ × w = 8 × 5 = 40 cm²

We have,

Volume of Rectangular Pyramid (V) = 1/3 × A × H

V = 1/3 × 40 × 14 = 560/3 = 186.67 cm³

Hence, volume of the given rectangular pyramid is 186.67 cm³.

Problem 5: What is the volume of a hexagonal pyramid if the sides of a base are 8 cm each and the height of the pyramid is 15 cm?

Solution:

Given

• Height of Pyramid = 15 cm
• Length of Side of Base of Hexagonal Pyramid = 6 cm

Area of Hxagonal Base (A) = 3√3/2 a² = 3√3/2 (6)² = 54√3 cm²

Volume of Hexagonal Pyramid (V) = 1/3 × A × H

V = 1/3 × 54√3 × 15 = 270√3 cm³

Hence, volume of the given hexagonal pyramid is  270√3 cm³.

Problem 6: What is the volume of a pentagonal pyramid if the base area is 150 cm² and the height of the pyramid is 11 cm?

Solution:

Given

• Area of Pentagonal Base = 150 cm²
• Height of Pyramid = 11 cm

Volume of Pentagonal Pyramid (V) = 1/3 × Area of Pentagonal Base × Height

V = 1/3 × 150 × 11 = 550 cm³

Hence, volume of the given pentagonal pyramid = 550 cm³

Pyramid is a three-dimensional shape whose base is a polygon, and all its triangular faces join at a common point called the apex. The pyramids of Egypt are real-life examples of pyramids. Volume of a pyramid is the space occupied by that pyramid and is calculated by the formula, V = 1/3×(Area of Base)×(Height)

In this article, we have covered Pyramid definition, volume of the pyramid formula, derivation and others in detail.