Question

Medal + fan
The volumes of two similar solids are 729m^3 and 125m^3. The surface area of the larger solid is 324m^2. What is the surface area of the smaller solid?
My Guess**A 56m^2
B 100m^2
C 500m^2
D 200m^2

Answer 1

What do you think?

Answer 2

If I had to guess?... A?

Answer 3

That's what it looks like the answer is.

Answer 4

I kind of want to go with B, but just stick with A for now

Answer 5

Why were you thinking b? @Erak

Answer 6

A kinda seems like the obvious answer

Answer 7

I see where @Erak is coming from.

Answer 8

Okay for the ratio between them because they are "similar solids", I will assume they are both cubes.

cbrt(729) = 9
cbrt(125) = 5

The sides are in a 9:5 ratio, or change of 1.8

324 = 6s^2
s = sqrt(54)

That's what I get for the sidelength, now to convert it to the smaller cube, divide by 1.8, so sqrt(54)/1.8

SA = 6s^2
SA = 6(sqrt(54)/1.8)^2
SA = 100m^2

Answer 9

@jim_thompson5910 want to check my reasoning?

Answer 10

The ratio of the volumes is 729:125

Take the cube root of both pieces to get 9:5

Notice how 9/5 = 1.8

So the length of the larger object is 1.8 times bigger than the corresponding length of the smaller object


I.E.
length of the larger object = 1.8*(length of the smaller object)


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Square 1.8 to get 3.24


Let
x = larger surface area
y = smaller surface area


The ratio of the surface areas is going to be

(larger surface area)/(smaller surface area) = 3.24
x/y = 3.24
324/y = 3.24
324 = 3.24y
y = 100

So you are correct. The smaller object has a surface area of 100 m^2

Answer 11

@jim_thompson5910 thank you, i knew it couldn't be as simple as A