solid geometry

Question

If the areas of three of the faces of a rectangular solid are 6,10 and 15 what is the volume of the solid ?

 

(a)10

(b)55

(c)20

(d)30

Answer 1

Draw a box and label adjacent faces with their areas.  Since the area of each face is the product of the side lengths that form the area of a rectangular face, label the sides with values so that when they are multiplied together, you get the area.  For the volume, multiply the length, width, and height.  The length, width, and height are the values you just labeled for your side lengths.  I cannot draw the actual box here, but the length, width, and height that I got was 2, 3, and 5.

 

2 × 3 = 6

2 × 5 = 10

3 × 5 = 15

 

Notice that adjacent areas share at least one side length.  Areas 6 and 10 share side length 2.  Areas 6 and 15 share the side length 3.  Areas 10 and 15 share the side length 5.

 

2 × 3 × 5 = 30

 

The volume is 30.