Question

The volumes of two similar solids are 729 inches3 and 125 inches3. If the surface area of the smaller solid is 74. 32 inches2, what is the surface area of the larger solid? Round to the nearest hundredth. 133. 78 in. 2 240. 80 in. 2 433. 43 in. 2 678. 32 in. 2.

Answer 1

The surface area of the larger solid, rounded to the nearest hundredth is given by: Option B: $240.80\: \rm inch^2$

How can we interpret volume of a solid?

Volume of a solid is usually expressed in cubic units, or units cube.

Suppose that the volume was expressed in x cubic units. Then you can say that the considered solid takes same space as the volume occupied by x cubes of 1 unit as their side lengths.

What are similar objects?

They're like zoomed version of each other(might be non-zoomed, zoomed in, or zoomed out). Their sides can be obtained by multiplying one object's sides by a single constant(by single constant, we mean constant which will be same for obtaining any corresponding side).

For the given case, we're given that:

• Volume of first solid = 729 cubic inches.
• Volume of second solid = 125 cubic inches.

Both solids are similar.

Thus, let the scale factor by which their sides change be 'f'.

Then, we get:

• Side of first solid = f × side of second solid

• Surface area of first solid(a square piece chosen on its surface) =  f × f × surface area of second solid

(as two times sides multiplied, so two times f got multiplied).

Similarly,

• volume of first solid =  f × f × f × volume of second solid.

Or

$729 = f^3 \times 125\\f = \: ^3\sqrt{\dfrac{729}{125}} = \dfrac{9}{5} = 1.8$

As surface area of smaller solid(second solid is smaller as its volume is less) is 74.32 sq. inches, and f = 1.8, thus, we get:

$S_{\text{larger solid}} = f^2 \times S_{\text{smaller solid}} = (1.8)^2 \times 74.32\\S_{\text{larger solid}} = 240.7968 \approx 240.80 \: \rm inch^3$

Thus, the surface area of the larger solid, rounded to the nearest hundredth is given by: Option B: $240.80\: \rm inch^2$

Learn more about volume and surface area here:

brainly.com/question/2952465