Question

Please help ASAP

If two similar solids have volumes of 1715 cm^3 and 320 cm^3.

a. Calculate the ratio of the surface areas

b. If the larger solid has a surface area of 196 cm^2, what is the surface area of the smaller solid.

Answer 1

a. The ratio of the surface areas of two similar solids is equal to the square of the ratio of their corresponding side lengths. Since volume is proportional to the cube of the side length, we can find the ratio of the side lengths by taking the cube root of the ratio of the volumes:

1715/320 = (x/y)^3

where x and y are the side lengths of the larger and smaller solids, respectively. Solving for x/y, we get:

x/y = (1715/320)^(1/3) = 2.5

So the ratio of the surface areas is:

(2.5)^2 = 6.25

b. We can use the same ratio of surface areas to find the surface area of the smaller solid:

196/6.25 = 31.36

So the surface area of the smaller solid is approximately 31.36 cm^2.