Question 3

A rectangular prism has dimensions 3 inches, 4 inches, and 5 inches. Find the dimensions of another
rectangular prism with the same volume but less surface area.

What are the dimensions of the shape? *

What is its surface area?*

Step-by-step explanation:

The formula for finding the volume is

Volume = length × width × height

Volume of the given prism is

Volume = 3 × 4 × 5 = 60 inches³

The formula for determining the surface area of a rectangular prism is expressed as

Surface area = Ph + 2B

Where

P represents perimeter of base

h represents height of prism

B represents base area

Perimeter of base = 2(length + width)

P = 2(3 + 4) = 14 inches

B = 3 × 4 = 12 inches

h = 5 inches

Surface area = 14 × 5 + 2 × 12 = 94 inches²

For another prism,

Assuming h = 3, length = 10 and width = 2, then

Volume = 3 × 10 × 2 = 60 inches³

P = 2(10 + 2) = 24 inches

B = 10 × 2 = 20 inches

Surface area = (24 × 3) + (2 × 20) = 112 inches²

If we keep changing the values, the surface area will always be greater than 94 inches².

Therefore, there is no rectangular prism with the same volume but less surface area.

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