Question

Eric used two similar cylinder shapes in his art project. One cylinder had a radius of 3.5 inches and a height of 8 inches. If the other cylinder had a radius of 5.25 inches, what was its height?

Answer 1

By using the ratio of corresponding linear dimensions of similar figures, we find that the height of the second cylinder with 5.25 inches radius is 12 inches, if the first cylinder has a radius of 3.5 inches and a height of 8 inches.

Step-by-step explanation:

The student asked what the height of the second cylinder would be if the first cylinder had a radius of 3.5 inches and a height of 8 inches, and the second one had a radius of 5.25 inches.

Since the cylinders are similar, we can use the property that the ratio of corresponding linear dimensions of similar figures is constant. This means that the ratio of the radii of the cylinders is the same as the ratio of their heights.

So, let's denote the unknown height of the second cylinder as h.

Using the ratio of corresponding dimensions, we get:

1. First Cylinder Radius : Second Cylinder Radius = First Cylinder Height : Second Cylinder Height
2. 3.5 inches : 5.25 inches = 8 inches : h
3. (3.5 / 5.25) = (8 / h)
4. h = (8 inches * 5.25 inches) / 3.5 inches
5. h = 12 inches

Therefore, the height of the second cylinder is 12 inches.