Question

A right rectangular prism has a base with an area of `25\ \frac{1}{2}`square feet and a volume of 153 cubic feet. What is the height, in feet, of the right rectangular prism?

Answer 1

Answer:

Height = 6 feet

Step-by-step explanation:

Given the following data;

Base area = 25½ ft²

Volume = 153 ft³

To find the height of the right rectangular prism;

Mathematically, the volume of a right rectangular prism is given by the formula;

Volume = base area * height

Substituting into the formula, we have;

153 = 25½ * height

153 = 51/2 * height

Cross-multiplying, we have;

306 = 51 * height

Height = 306/51

Height = 6 feet

Answer 2

Right rectangular prism is also called cuboid. The height of the right rectangular prism considered is evaluated as of 6 ft

How to find the volume of a right rectangular prism?

Suppose that the right rectangular prism in consideration be having its dimensions as 'a' units, 'b' units, and 'c' units, then its volume is given as:

$V = a\times b \times c \: \: unit^3$

For this case, we're provided that:

• Base area of the right rectangular prism = $25\dfrac{1}{2} = 25 + 0.5 = 25.5 \: \rm ft^2$
• Volume of the right rectangular prism = $153\: \rm ft^3$

Let the length and width of the prism be L ft and W ft

Let the heigth of the prism be H ft

Then, we get:

• Area of base = $L \times W = 25.5 \: \rm ft^2$ (since base is a rectangle with length L and width W).
• Volume of prism = $V = H \times L \times W = H \times 25.5 = 153 \: \rm ft^3$

Thus, we get:
$H \times 25.5= 153\\\\\text{Dividing both the sides by 25.5}\\\\H = \dfrac{153}{25.5} = 6 \: \rm ft$

Thus, the height of the right rectangular prism considered is evaluated as of 6 ft.

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