Question

Complete the table with the ratios of the base areas, surface areas, and volumes of these two similar cones. Assume the ratios are written in the form cone A : cone B. Two diagrams depict a small cone labeled cone A and a large cone labeled cone B. The cone A has a vertex labeled O, height 5 units and radius on the base M N. The cone B has a vertex labeled G, height 15 units and radius E F.

Answer 1

To find the ratios of the base areas, surface areas, and volumes of the two similar cones, we can use the following formulas:

Ratio of base areas = (radius of cone A)^2 : (radius of cone B)^2

Ratio of surface areas = (surface area of cone A) : (surface area of cone B)

Ratio of volumes = (volume of cone A) : (volume of cone B)

Using the given dimensions, we can calculate the ratios as follows:

Ratio Calculation Simplified

Base areas (MN^2 : EF^2) 1 : 9

Surface areas (πMN(MN + ON) : πEF(EF + FG)) 1 : 3

Volumes (1/3 x πMN^2 x ON : 1/3 x πEF^2 x FG) 1 : 27

Therefore, the ratios of the base areas, surface areas, and volumes of the two cones are 1 : 9, 1 : 3, and 1 : 27, respectively.