&KDSWHU 0RUH(QULFKPHQW7RSLFVIn exercises 1–3, the pair of solids is similar.
Find each of the following:
a. the ratio of similarity of the first solid to the second solid
b. the surface areas and the ratio of the surface areas (first solid to second solid)
c. the volumes and the ratio of the volumes (first solid to second solid)
1.Cylinder E: radius 7 cm, height 14 cm
Cylinder F: radius 14 cm, height 28 cm
2.Square pyramid G: length 6 ft, face height 5 ft
Square pyramid H: length 30 ft, face height 25 ft3.Cone J: radius 20 in., height 48 in., slant height 52 in.
Cone K: radius 5 in., height 12 in., slant height 13 in.4.Discuss and Write Refer to your results from exercises 1–3. How
does the ratio of the surface areas of each pair of solids relate to
the ratio of similarity? How does the ratio of the volumes of each
pair of solids relate to the ratio of similarity for the two solids?pages 365–366 for exercise sets.Prism 1 in the drawing has edges that are half as long as those
in Prism 2, so the ratio of similarity is 1 : 2.
Calculate the surface areas of the prisms you drew.
Remember, the surface area is the sum of the areas
of the faces. Then find the ratio of the surface areas.
For Prisms 1 and 2, the results are shown below.
How does 1 : 4 relate to the ratio of similarity, 1 : 2?
1 : 4 can be written as 1^2 : 2^2 , the square of the ratio of similarity.
For these two similar prisms (and for all similar prisms), the ratio
of surface areas is the square of the ratio of similarity.
Now, calculate the volumes of your prisms. Then
find the ratio of the volumes. For Prisms 1 and 2,
the results are shown at the right.
How does this ratio relate to the ratio of similarity, 1 : 2?
The ratio is 1 : 8 and can be written as 1^3 : 2^3. For these two similar
prisms (and for all similar prisms), the ratio of volumes is the cube
of the ratio of similarity.
Prism Surface Area Ratio
1 52 units^2 52 : 208 or
2 208 units^2 1:4Prism Volume Ratio
1 24 units^3 24 : 192 or
2 192 units^3 1 : 8