Question

The scale of two similar solids is 6:13. Determine the following: the ratio of their corresponding areas and the volume of the larger solid if the volume of the smaller solid is 432in^2

Answer 1

Scale is a one-to-one measure, which can be used as a perimeter measure if needed. Area, then, takes this one-to-one and squares it, because area is a squared measure (whereas perimeter is a single unit measure). Volume is a cubed measure. To find the ratio of the areas, we will take the one-to-one ratio and square it:
`( (6)/(13) ) ^(2) = (36)/(169)`. To find the volume ratio, take the same one-to-one and cube it:
`( (6)/(13)) ^(3) = (216)/(2197)`. Now we can set up a proportion using the smaller volume. The smaller of the values for the volume is on top and the larger is on bottom:
`(216)/(2197)= (432)/(x)`. Cross-multiply to get 216x=949104. Solving for x will give us the larger volume: x = 4394