Question

The areas of the faces of a rectangular box are 84 sq cm, 70 sq cm and 30 sq cm. What is the volume of the box?

1-8820 cu cm
2-420 cu cm
3-2400 cu cm
4-can not be determined​

Answer 1

Answer: 420 cm3

Step-by-step explanation:

et x, y, and w represent the three length of the sides of the rectangular box.

Then you can write the following equations:

xy = 84

xw = 70

and yw = 30.

Then w = 70 / x and substitute it in equation 3 to obtain   70y / x = 30.

Solving for x, we get x = 70y / 30.

Substitute this in equation #1 to get   70y2 / 30 = 84

This yields y2 = 36, so y = 6 cm.

It follows that x = 14 cm and w = 5 cm.

Therefore, the volume is 6 x 14 x 5 = 420 cm3

hope it helpful