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.
18/6 = 3/1 = 3:1
Therefore, the ratio of the radii of the cylinders is 3:1.
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 X is similar to Solid Y by a scale factor, then the surface area of X is equal to the surface area of Y times the square of the scale factor.
Therefore, to get the surface area of Cylinder A, we need to multiply the surface area of Cylinder B by the scale factor raised to the second power. In Part A, we found that the ratio of the radii of the cylinders is 3:1. This means that the scale factor is 3.
S.A. of Cylinder A
=
3^2 ( S.A. of Cylinder B)We can rewrite this equation to get the ratio of the surface area of Cylinder A to the surface area of Cylinder B.
The ratio of the surface areas of the cylinders is 9:1. 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 X is similar to Solid Y by a scale factor, then the volume of X is equal to the volume of Y times the cube of the scale factor.
Therefore, to get the volume of Cylinder A, we need to multiply the volume of Cylinder B by the scale factor raised to the third power.
Volume of Cylinder A
=
3^3 ( Volume of Cylinder B)
We can rewrite this equation to get the ratio of the volume of Cylinder A to the volume ofCylinder B.
Volume of Cylinder A = 3^3 (Volume of the Cylinder B)
The ratio of the volumes of the cylinders is 27:1.
In Part B, we found that the ratio of the surface areas of the cylinders is 9:1.
S.A. of Cylinder A/S.A. of Cylinder B = 9:1
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!
We got that the surface area of Cylinder B is 602.88 cm^2.
In Part B, we found that the ratio of the volumes of the cylinders is 27:1.
Volume of Cylinder A/Volume of Cylinder B = 27:1
Since we know the volume of Cylinder B, we can calculate the volume of Cylinder A using this ratio. Let's do it!
