Glencoe Math: Course 3, Volume 2
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Glencoe Math: Course 3, Volume 2 View details
6. Changes in Dimensions
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Exercise 23 Page 647

Practice makes perfect

We are given two similar solids.

The cylinders
We want to find the of ratio of the radii of the cylinders. To do so, we will divide the radius of Cylinder A by the radius of Cylinder B.
Therefore, the ratio of the radii of the cylinders is

Now we want to find the ratio of the surface areas and volumes of the given cylinders. Let's start with the ratio of the surface areas. To do so, we will recall the relationship between the surface areas of similar solids.

Surface Area of Similar Solids

If Solid is similar to Solid by a scale factor, then the surface area of is equal to the surface area of times the square of the scale factor.

Therefore, to get the we need to multiply the by the raised to the In Part A, we found that the ratio of the radii of the cylinders is This means that the is
We can rewrite this equation to get the ratio of the to the
The ratio of the surface areas of the cylinders is Next, we will find the ratio of their volumes. To do so, we will recall the relationship between the volumes of similar solids.

Volume of Similar Solids

If Solid is similar to Solid by a scale factor, then the volume of is equal to the volume of times the cube of the scale factor.

Therefore, to get the we need to multiply the by the raised to the
We can rewrite this equation to get the ratio of the to the
The ratio of the volumes of the cylinders is
In Part B, we found that the ratio of the surface areas of the cylinders is
Since we know the surface area of Cylinder A, we can calculate the surface area of Cylinder B using this ratio. Let's do it!
Solve for
We got that the surface area of Cylinder is
In Part B, we found that the ratio of the volumes of the cylinders is
Since we know the volume of Cylinder B, we can calculate the volume of Cylinder A using this ratio. Let's do it!
Solve for
We got that the volume of Cylinder is