Question

The volumes of two similar solids are 857.5 mm^3 and 540 mm^3. The surface area of the smaller solid is 108 mm^2. What is the surface area of the larger solid?(1 point) Responses 216 mm2 216 mm squared 147 mm2 147 mm squared 16 mm2 16 mm squared 68 mm2

Answer 1

To find the surface area of the larger solid, we first need to find the scale factor between the two similar solids.

Volume ratio = (Volume of larger solid) / (Volume of smaller solid)
Volume ratio = 857.5 mm^3 / 540 mm^3
Volume ratio = 1.587

Since the volume ratio is equal to the cube of the scale factor, we can find the scale factor by taking the cube root of the volume ratio:

Scale factor = cuberoot(1.587)
Scale factor ≈ 1.2

Now, we can use the scale factor to find the surface area ratio and then find the surface area of the larger solid:

Surface area ratio = (Scale factor)^2
Surface area ratio = 1.2^2
Surface area ratio = 1.44

Surface area of the larger solid = Surface area of the smaller solid * Surface area ratio
Surface area of the larger solid = 108 mm^2 * 1.44
Surface area of the larger solid = 155.52 mm^2

Therefore, the surface area of the larger solid is approximately 155.52 mm^2. The closest answer option is 147 mm^2.