The volume of 2 similar solids are 27 ft3 and 216 ft3. The surface area of the larger solid is 300 ft2. What is the surface area of the smaller solid? Round your answer to the nearest tenths place

To find the surface area of the smaller solid, we can use the concept of similarity. Since the solids are similar, the ratio of their volumes is equal to the cube of the ratio of their corresponding lengths.

Let's represent the ratio of their lengths as "x". Therefore, the ratio of their volumes is x³.

Given that the volume of the larger solid is 216 ft³ and the volume of the smaller solid is 27 ft³, we can set up the following equation:

x³ = 216/27

Simplifying this equation gives us:

x³ = 8

Taking the cube root of both sides, we find:

x = ∛(8)

x = 2

This means that the lengths of the two solids are in a 1:2 ratio.

Now, we can find the surface area of the smaller solid. Since the surface area of a solid is proportional to the square of its length, we can set up the following equation:

(smaller surface area) / (larger surface area) = (smaller length)² / (larger length)²

Let's represent the surface area of the smaller solid as "S" and the surface area of the larger solid as 300 ft². We already know that the lengths are in a 1:2 ratio. Let's assume the length of the larger solid is 2L and the length of the smaller solid is L.

The equation becomes:

S / 300 = L² / (2L)²

Simplifying this equation gives us:

S / 300 = L² / 4L²

Cross-multiplying, we find:

S * 4L² = 300 * L²

Simplifying further:

4SL² = 300L²

Dividing both sides by L²:

4S = 300

S = 300 / 4

S = 75

Therefore, the surface area of the smaller solid is approximately 75 ft² when rounded to the nearest tenths place.

volume ratio = 216/27, and is the cube of the linear scale factor.

So, each side of the larger is 6/3 = 2 times the smaller.

So, the area of the larger is 2^2 = 4 times the smaller.