b Recall the relationship between the scale factor of two similar solids and the ratio of their areas.
A
a 11:14
B
b 121 : 196
Practice makes perfect
a The volumes of two similar pyramids are 1331 cm^3 and 2744 cm^3. We want to first find the ratio of their height. The ratio of the heights is the same as the ratio of the scale factor. Let's recall the Areas and Volumes of Similar Solids Theorem.
Areas and Volumes of Similar Solids Theorem
If the scale factor of two similar solids is ab or a:b then the ratio of their volumes is a^3b^3 or a^3:b^3.
This means that we can form a ratio out of the given volumes of the pyramids and the cube root of this ratio will be equal to the scale factor. Let a^3= 1331 for the volume of the small pyramid, and let b^3= 2744 for the volume of the larger sphere.
The ratio of their heights and their scale factor is 11:14.
b Now that we know that the scale factor for the two pyramids we can find the ratio of their surface areas by again using the Areas and Volumes of Similar Solids Theorem.
If we let a= 11 and b= 14, the ratio of the squares of a and b will be the ratio of the surface areas of the pyramids.
