Question

31. 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? (1 point)
81
121
305
405
I think it's C.

Answer 1

Did they give you a drawing or any other information?

Answer 2

No. That's all that's given. These are practice problems I found to help me.

Answer 3

Assume the larger solid has a volume calculated by length times width times height.\\[V_{larger} = whl\]\]Let the smaller solid have a volume calculated by length times width times height, but these measurements are some factor k smaller than the similar measurements of the larger solid.\[V_{smaller}=(kw)(kh)(kl)=k^3whl=k^3V_{larger}\]

Answer 4

Assume the surface area of the larger solid has a surface area calculated by \[A_{larger}=2wl+2lh+2wh=2(wl+lh+wh)\]The surface area of the smaller solid would be given by\[A_{smaller}=2(kw)(kl)+2(kl)(kh)+2(kw)(kh)=k^2[2(wl+lh+wh)]=k^2A_{larger}\]

Answer 5

Now\[V_{smaller}=k^3V_{larger}\]\[k^3=\frac{V_{smaller}}{V_{larger}}\]Likewise we have\[k^2=\frac{A_{smaller}}{A_{larger}}\] Plug the value for the volumes into the first equation and solve for k. Plug the values for the area and k into the second equation and solve for the area of the smaller solid.

Answer 6

\[\sqrt[3]{1331}=11\]\[\sqrt[3]{729}=9\]
\[9^{2}=81\]

Answer 7

Sq Meters

Answer 8

Oh, okay! That makes sense now. Thanks so much!

Answer 9

Not knowing the shapes of the solid, just that they are similar, that is the best I can come up with.