Sign In
3:1
Ratio of the Surface Areas: 9:1
Ratio of the Volumes: 27:1
602.88 cm2
30520.8 cm3
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. |
LHS/(S.A. of Cylinder B)=RHS/(S.A. of Cylinder B)
Calculate power
a=1a
ba=a:b
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. |
LHS/(Volume of Cylinder B)=RHS/(Volume of Cylinder B)
Calculate power
a=1a
ba=a:b
S.A. of Cylinder A=5425.92
a:b=ba
1a=a
LHS⋅(S.A. of Cylinder B)=RHS⋅(S.A. of Cylinder B)
S.A. of Cylinder Ba⋅S.A. of Cylinder B=a
LHS/9=RHS/9
Cancel out common factors
Simplify quotient
Calculate quotient
Rearrange equation
Volume of Cylinder B=1130.4
a:b=ba
1a=a
LHS⋅1130.4=RHS⋅1130.4
1130.4a⋅1130.4=a
Multiply