Examples on Square Prism formula

Example 1: Find the volume of a square prism whose side is 8 cm and whose height is 13 cm.

Solution:

Given data,

• Length of side of a square prism (a) = 8 cm
• Height of a square prism (h) = 13 cm

We know that,

Volume of a square prism = a²h cubic units

= (8)² × 13

= 64 × 13

= 832 cu. cm

Thus, the volume of the given prism is 832 cu. cm.

Example 2: Calculate the surface area of a square prism whose side is 10 units and whose height is 15 units.

Solution:

Given data,

• Length of the side of a square prism (a) = 10 units
• Height of a square prism (h) = 15 units

We know that,

From the square prism formula, we have

Surface Area of a Square Prism = 2a² + 4ah square units

= 2(10)² + (4 × 10 × 15)

= 2(100) + 600

= 200 + 600 = 800 square units

Thus, the surface area of the given prism is 800 square units.

Example 3: Find the volume of a container whose shape is a square prism with a side of 20 inches and a height of 25 inches.

Solution:

Given data,

• Length of side of a square prism (a) = 20 inches
• Height of a square prism (h) = 25 inches

We know that,

Volume of a Square Prism = a²h cubic units

= (20)² × 22

= 400 × 25

= 1000 cu. in

Thus, volume of the given prism is 1000 cu. in.

Example 4: Calculate the lateral surface area of a square prism whose side is 12 cm and whose height is 16 cm.

Solution:

Given data,

• Length of the side of a square prism (a) = 12 cm
• Height of a square prism (h) = 16 cm

From the square prism formula, we have

Lateral surface area of a square prism = 4ah square units

= 4 × 12 × 16 = 768 sq. cm

Thus, the lateral surface area of the given prism is 768 sq. cm.

Example 5: Determine the height of a square prism if its volume is 891 cubic units and its side length is 9 units.

Solution:

Given data,

• Length of the side of a square prism (a) = 9 units
• Volume (V) = 891 cubic units

Height (h) =?

From the square prism formula, we have

Volume of a square prism = a²h cubic units

⇒ (9)² × h = 891

⇒ 81h = 891

⇒ h = 891/81 = 11 units

Hence, the height of a square prism is 11 units.

Example 6: Determine the side length of a square prism if its lateral surface area is 660 sq. cm and its height is 15 cm.

Solution:

Given data,

• Height of a square prism (h) = 15 cm
• Lateral surface area = 660 sq. cm

Length of the side of a square prism (a) =?

From the square prism formula, we have

Lateral surface area of a square prism = 4ah square units

⇒ 4 × a × 15 = 660

⇒ 60a = 660

⇒ a = 660/60 = 11 cm.

Hence, the side length of the given prism is 660 sq. cm.

A square prism is a three-dimensional shape cuboid figure whose bases are squares and the other four faces are rectangular. It also called a rectangular prism or cuboid, is a three-dimensional geometric shape characterized by having two congruent square bases and four rectangular faces perpendicular to the bases.

We have different types of prisms based on the shape of the polygonal base, namely, triangular prisms, square prisms, rectangle prisms, Pentagonal prisms, hexagonal prisms, octagonal prisms, etc.

In this article, we will learn about, Square Prism Definition, Square Prism Formulae, Examples and others in detail.