Answer: 8/343
Step-by-Step:
If two similar solids have a scale factor of a:b then,
The ratio of their surface areas (2D) is- a^2:b^2
The ratio of their volume (3D) is- a^3:b^3
First you want to square root the scale factor numbers to find the original value. Then you cube the original numbers to find the answer.
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Work Shown:
Check out the diagram below. Note the pair of alternate interior angles that are congruent (each 37 degrees). Then focus on triangle ABC. With the reference angle being at A, this means we use the tangent function because BC = x is the opposite side and AB = 97 is the adjacent side.
tan(angle) = opposite/adjacent
tan(A) = BC/AB
tan(37) = x/97
97*tan(37) = x
x = 97*tan(37)
x = 73.094742859971
For the last step, you'll need a calculator that can handle trig functions. Make sure the calculator is in degree mode. The result here is approximate. This rounds to 73 when rounding to the nearest whole number.
