Question

The volume of two similar solids is 1331 m3 and 729 m3. The surface area of the larger solid is 605 m2.

What is the surface area, in square meters, of the smaller solid?

Answer 1

121

305

405

81

Answer 2

The King George

Answer 3

tips?

Answer 4

proportions?

Answer 5

Definitely proportions, but in a certain way. Notice that the volume of two solids is proportional to the cube of the side lengths, while the surface area is proportional to the square of the side lengths.

Answer 6

hmm

Answer 7

So what I would do is find the proportion for the side lengths, and then square it to find the proportion of the surface area. Once you have that, you can simply plug 605m\(^2\) into the proportion.

Answer 8

ehh

Answer 9

well

Answer 10

the cube root of 1331 is 11 while the cube root of 729 is 9

Answer 11

does that help any?

Answer 12

That's great so far. The ratio of the side lengths would then be 11/9. So the ratio of the surface areas is...?

Answer 13

605/x

Answer 14

I got 495

Answer 15

thats not an answer choice , though :(

Answer 16

I don't think you used the correct proportions there. If the proportion for side length is 11/9, and the proportion for surface area is the square of the proportion for side length, what is that proportion?

Answer 17

11/605?

Answer 18

605/11=55

Answer 19

Not quite, sorry if I wasn't very clear with I said. It should be\[\left(\frac{11}{9}\right)^2=\frac{121}{81}\]

Answer 20

AHH

Answer 21

THE AREA

Answer 22

121/81=605/x

Answer 23

405

Answer 24

Precisely.

Answer 25

next problem

Answer 26

9^3/11^3
so the area ration will be 9^2/11^2
9^2/11^2*605=405