Exercise 35 Page 73

Let's calculate the volume of the original prism and the volume of the prism with the doubled dimensions, and then compare them.

Volume of the Original Prism

In order to calculate the volume of the prism we can use the determined formula. V=wl h Here w is the width, l is the length, and h is the height of the prism. We are given that the rectangular prism has a width of 18 cm, a length of 12 cm, and a height of 22 cm. By substituting these values into the formula we can calculate the prism's volume.

The volume of the original prism is 4752cm^3.

Volume of the Increased Prism

After the dimensions of the original prism are doubled, we get the following new dimensions. { lw=18cm l=12cm h=22cm ⇒ { lw=18* 2= 36cm l=12* 2= 24cm h=22* 2= 44cm Let's again substitute these values into the volume formula and calculate V_(increased).

The volume of the increased prism is 38 016cm^3.

Conclusion

Let's now compare the found volumes of the original and increased prism. V_(original)=4752 cm^3 V_(increased)=38 016 cm^3 To find how much the volume of the increased prism is greater that the volume of the original prism, we can divide the second value by the first one.

Therefore, after each dimension of the prism was doubled, its volume increased by a factor of 8.