Question

Help? Step by step pls?

Answer 1

The depth of the orange juice is 4 cm now.

Explanation:

Volume of a Rectangular Prism or Cuboid

A rectangular prism (cuboid, or a box as we commonly call it) with a width W, length L, and height H has a volume of:

`V = WLH`

Note WL is the area of the base Ab=WL, thus:

`V = A_bH`

Jane has a carton of orange juice of dimensions:

W=6 cm

L = 10 cm

H = 20 cm

It's actually filled with h=8 cm of orange juice, thus the volume of juice is:

`V_j=6*10*8=480\ cm^3`

When Jane turns the carton over the shaded face (the one with a base of 6 cm by 20 cm), the volume of juice is, of course, the same, but the new height can be calculated by finding the new area of the base:

`A_b=6*20=120\ cm^2`

The volume of the juice when turned over is:

`V_j=A_b.H'`

Where H' is the required height. Solving for H':

`\displaystyle H'=(V)/(A_b) =(480)/(120)=4\ cm`

The depth of the orange juice is 4 cm now.