The volumes of 2 similar solids are 27pi and 125pi . The surface area of the larger solid is 250pi. What is the surface area of the smaller solid? Round your answer to the tenths place.

*question has been edited by a moderator to supply missing information*

Question

The volumes of 2 similar solids are 27pi and 125pi . The surface area of the larger solid is 250pi. What is the surface area of the smaller solid? Round your answer to the tenths place.

*question has been edited by a moderator to supply missing information*

Tranquility · Answer

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Vocaloid · Answer

I have supplied the missing information from the problem if you still want to attempt the question

Tranquility · Answer

The volumes of 2 similar solids are 27pi and 125pi . The surface area of the larger solid is 250pi. What is the surface area of the smaller solid? Round your answer to the tenths place.

Since we are working with similar solids, we can use the ratio of their sides to solve the question.

The larger solid has a volume of 125pi and a surface area of 250pi
The smaller solid has a volume of 27pi and a surface area of 'x' which we are solving for

If you tried to set it up as 
125pi/27pi = 250pi/x

Then you would get the wrong answer. That's because the volume and surface area don't form a ratio.

The ratio of the surface areas is equal to the SQUARE of the ratio of their corresponding side length
On the other hand, the ratio of the volumes is equal to the CUBE of the ratio of their corresponding side lengths

What this means is
If we call the bigger solid A, and the smaller solid B
$\Large \sf \frac{SA_A}{SA_B} = (\frac{a}{b})^2$

$\Large \sf \frac{V_A}{V_B} = (\frac{a}{b})^3$

$\sf SA_A$ is the surface area of the bigger solid A
$\sf SA_B$ is the surface area of the smaller solid B
$\sf V_A$ is the volume of the bigger solid A
$\sf V_B$ is the volume of the smaller solid B

Since we have $\sf SA_A$ and $\sf SA_B$, first solve for a and b. Then plug that into the second formula along with $\sf V_A$ to solve for $\sf V_B$.

Let me know if you understood so far and how far you get in your attempt at solving this question @TahjGibson