Question

A company makes concrete paving stones in different sizes. Each stone has a volume of 30 cubic inches and a height of 3 inches. The stones have different lengths and width. No stone have a length or width of 1 or 2 inches. How many different paving stones, each with a different-size base, have a volume os 360 cubic inches?

Answer 1

Answer:

There are 5 different sized paving stones that can have a volume of 360 in³.

Step-by-step explanation:

Volume = Area x height.

We are given;

volume; V = 360 in³

Height; h = 3 in

Thus, 360 = A x 3

A = 360/3 = 120 in²

This is the area of the base, so we need to find the number of different stones which have a base area of 120 in².

Let's list all the factors of 120 which are;

1,2,3,4,5,6,10,12,20,24,30,40,60,120

The question says we shouldn't use 1 or 2 in inches as length and width.

Leaving us with the remaining listed factors.

So the pair of factors that give and area of 120 are;

Size;

3 x 40

4 x 30

5 x 24

6 x 20

10 x 12

Thus, there are 5 different sized paving stones that can have a volume of 360.