The surface areas of two similar solids are 311 ft2 and 1,037 ft2. the volume of the larger solid is 1,755 ft3. what is the volume of the smaller solid?

Answering

Ratio of surface areas is equal to the square of the corresponding dimensions and ratio of volumes of the two solids is equal to the cube of the ratio of the dimensions of the two solids .

Using that information , and let a and b are the corresponding sides of the two solids , we will get

Now we need to get rid of the square. And for that, we take square root to both sides,

\sqrt{\frac{311}{1037}}=\frac{a}{b}

Let the volume of the smaller solid be x .

So we will get

\frac{x}{1755}=(\sqrt{\frac{311}{1037}} )^3

x = 1755(\sqrt{\frac{311}{1037}})^3

x=288 ft approx

So the volume of the smaller solid = 288 ft approx

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