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Varvara68 [4.7K]
2 years ago
14

The volumes of two similar solids are 729 inches3 and 125 inches3. If the surface area of the smaller solid is 74. 32 inches2, w

hat 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.
Mathematics
1 answer:
Lelu [443]2 years ago
8 0

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

<h3>How can we interpret volume of a solid?</h3>

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.

<h3>What are similar objects?</h3>

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

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