A juice box shaped like a rectangular prism has a length of 5.25 cm, and a height that is 2 cm longer than three times its width.

Write an equation that represents the volume of the juice box.

Recall that the formula for the volume of a rectangular prism is V = l · w · h, where l represents the length, w represents the width, and h represents the height.

Answer:V=15.75w^2+10.5w

Step-by-step explanation:

V=l*w*h

So,

V = (5.25) (w) (3w+2)

=5.25w (3w+2)

=15.75w^2+10.5w

V = 15.75w² + 10.5w

Step-by-step explanation:

A rectangular prism is the same as a cuboid and the volume of a cuboid is length multiplied by width multiplied by the height.

And we were provided with the following:

Length = 5.25cm

Width is unknown, = w

The height is said to be 2cm longer than 3 times it's width.

The above statement can be mathematically represented as;

H = 3w + 2

Apply the above into the formula given and we have

5.25 * w * (3w + 2)

Expand the above and we have

V = 5.25w * (3w + 2)

V = 15.75w² + 10.5w