We have two similar cylinders whose heights are 23 cm and 8 in.
Given that the volume of the first cylinder is 552π cm^3, we will find the volume of the second cylinder. Let's first find the scale factor of the cylinders. To do so we will convert inches to centimeters using the fact that 1 inch is equal to 2.54 centimeters.
8 in. * 2.54cm/in.=20.32 cm
Now we can find the scale factor. The ratio of the height of the first cylinder to the height of the second cylinder will give us the scale factor.
Scale Factor
23/20.32≈ 1.13 ⇔ 1.13 : 1
The scale factor is about 1.13:1. Next, we will recall Theorem 12.1 to relate the scale factor to the ratio of the volumes..
Theorem 12.1
If two similar solids have a scale factor of a:b, then the ratio of the surface areas is a^2:b^2, and the ratio of the volumes is a^3:b^3.
By this theorem, we can find the ratio of the volumes of the solids.
c|c
Scale Factor & Ratio of the Volumes
1.13:1 & 1.45:1
From here we can write a proportion to find the volume of the second cylinder, V.
552π/V=1.45/1
Finally, let's solve this proportion for V.
