Question

An aquarium in the shape of a rectangular prism has a bottom, no top, two square sides, and two sides
the same height as the square sides but twice their length. The total area of the five sides 15 2,592 in?.
Find the volume of the aquarium. Complete the explanation of your reasoning.
Let x represent the length and height of the square sides. Then the longer sides and the bottom measure
2x by x. The total area of the five sides, in terms of x, is A =____
So, the total area of the five sides,
A, is 2,592 in2. Solving for x we get x =____
The tank's volume is ____
in squared?

Answer 1

Answer:

volume = 11,664 units cubed

Step-by-step explanation:

2$x^{2}$ times 3 = bottom and sides

$x^{2}$ times 2 = ends

A = 6$x^{2}$ + 2$x^{2}$ = 8$x^{2}$

2592 = A

2592/8 = 8$x^{2}$/8

324 = $x^{2}$

take square root of both sides

18 = x

so volume = length times width times height

2(18) times 18 times 18 = 11664

11664 units cubed