contestada

Lance has an aquarium in the shape of a rectangular prism completely filled with water that has a base area of 65 in² and a height of 12 in. Lance pours all of its contents into a second aquarium, also in the shape of a rectangular prism, that has a height of 3 in. The water completely fills the second aquarium.

What is the base area of this second aquarium?

Enter your answer in the box.

Respuesta :

akposevictor

The base area of the second aquarium is 260 in².

To solve this problem, recall the volume of a rectangular prism. Thus:

Volume of rectangular prism (V) = base area (BA) Ă— height (h)

  • Given:

Base area of first aquarium = 65 in²

Height of first aquarium = 12 in

Base area of second aquarium = [tex]x[/tex]

Height of second aquarium = 3 in

  • Therefore:

Volume of first aquarium (V1) = [tex]65 \times 12 = 780 in^{3}[/tex]

Volume of the second aquarium (V2) = [tex]x \times 3 = 3x in^{3}[/tex]

To find the value of [tex]x[/tex] (base area of the second aquarium) set both volumes equal to each other.

  • Thus:

[tex]3x = 780\\[/tex]

Divide both sides by 3

[tex]\frac{3x}{3} = \frac{780}{3} \\x = 260[/tex]

Therefore, the base area of the second aquarium is 260 in².

Learn more about volume of rectangular prism here:

https://brainly.com/question/16065525

Otras preguntas