The surface area of the larger solid, rounded to the nearest hundredth is given by: Option B:
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
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:
Thus, the surface area of the larger solid, rounded to the nearest hundredth is given by: Option B:
Learn more about volume and surface area here: