A rectangular prism and cube have equal volumes. The length of the rectangular prism is 12 centimeters (cm) and its width is 8cm. If each side of the cube is 12cm, then what is the height of the rectangular prism in centimeters?

Calculate Volume of Cube: Calculate the volume of the cube. Since the side of the cube is 12 cm, the volume of the cube (V_cube) is the side length cubed. V_cube = 12 cm * 12 cm * 12 cm V_cube = 1728 cubic centimetersFind Volume of Rectangular Prism: Use the volume of the cube to find the volume of the rectangular prism. Since the volumes are equal, the volume of the rectangular prism (V_prism) is also 1728 cubic centimeters. V_prism = V_cube V_prism = 1728 cubic centimetersCalculate Height of Prism: Calculate the height of the rectangular prism using its volume. The volume of a rectangular prism is given by the formula V_prism = length * width * height. We know the length (12 cm) and width (8 cm) of the prism, so we can solve for the height (h). 1728 cm³ = 12 cm * 8 cm * hIsolate Height in Equation: Divide both sides of the equation by the product of the length and width to isolate the height. h = 1728 cm³ / (12 cm * 8 cm) h = 1728 cm³ / 96 cm² h = 18 cm

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

A rectangular prism and cube have equal volumes. The length of the rectangular prism is 12 centimeters
(cm) and its width is
8cm. If each side of the cube is
12cm, then what is the height of the rectangular prism in centimeters?

A rectangular prism and cube have equal volumes. The length of the rectangular prism is $12$ centimeters $(\mathrm{cm})$ and its width is $8 \mathrm{~cm}$ . If each side of the cube is $12 \mathrm{~cm}$ , then what is the height of the rectangular prism in centimeters?

View step-by-step help

Full solution

Q. A rectangular prism and cube have equal volumes. The length of the rectangular prism is

12

centimeters

(\mathrm{cm})

and its width is

8 \mathrm{~cm}

. If each side of the cube is

12 \mathrm{~cm}

, then what is the height of the rectangular prism in centimeters?

Calculate Volume of Cube: Calculate the volume of the cube. $\newline$ Since the side of the cube is $12\,\text{cm}$ , the volume of the cube ( $V_{\text{cube}}$ ) is the side length cubed. $\newline$ $V_{\text{cube}} = 12\,\text{cm} \times 12\,\text{cm} \times 12\,\text{cm}$ $\newline$ $V_{\text{cube}} = 1728\,\text{cubic centimeters}$
Find Volume of Rectangular Prism: Use the volume of the cube to find the volume of the rectangular prism. Since the volumes are equal, the volume of the rectangular prism $V_{\text{prism}}$ is also $1728$ cubic centimeters. $V_{\text{prism}} = V_{\text{cube}}$ $V_{\text{prism}} = 1728 \text{ cubic centimeters}$
Calculate Height of Prism: Calculate the height of the rectangular prism using its volume. The volume of a rectangular prism is given by the formula $V_{\text{prism}} = \text{length} \times \text{width} \times \text{height}$ . We know the length $(12 \, \text{cm})$ and width $(8 \, \text{cm})$ of the prism, so we can solve for the height $(h)$ . $1728 \, \text{cm}^3 = 12 \, \text{cm} \times 8 \, \text{cm} \times h$
Isolate Height in Equation: Divide both sides of the equation by the product of the length and width to isolate the height. $\newline$ $h = \frac{1728 \, \text{cm}^3}{(12 \, \text{cm} \times 8 \, \text{cm})}$ $\newline$ $h = \frac{1728 \, \text{cm}^3}{96 \, \text{cm}^2}$ $\newline$ $h = 18 \, \text{cm}$