Respuesta :
The surface area of the larger solid, rounded to the nearest hundredth is given by: Option B: [tex]240.80\: \rm inch^2[/tex]
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
[tex]729 = f^3 \times 125\\f = \: ^3\sqrt{\dfrac{729}{125}} = \dfrac{9}{5} = 1.8[/tex]
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:
[tex]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[/tex]
Thus, the surface area of the larger solid, rounded to the nearest hundredth is given by: Option B: [tex]240.80\: \rm inch^2[/tex]
Learn more about volume and surface area here:
https://brainly.com/question/2952465
