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
16 mm2
68 mm2
147 mm2

Answer 1

[AI-generated answer — Bot GPT 3.5]

147 mm2

To find the surface area of the larger solid, we can use the ratio of their volumes to find the ratio of their side lengths, and then calculate the surface area.

Let the side length of the smaller solid be x and the side length of the larger solid be y.

We have:
(Volume large solid) / (Volume small solid) = (y^3) / (x^3) = 857.5 / 540
y^3 = (857.5 / 540) * x^3
y^3 = 1.587*x^3
y = 1.077*x

Now, to find the surface area of the larger solid, we use the ratio of side lengths to find the ratio of their surface areas:
(Surface area large solid) / (Surface area small solid) = (y^2) / (x^2) = (1.077*x)^2 / x^2 = 1.16
(Surface area large solid) = 1.16 * 108 mm^2 = 125.28 mm^2

Therefore, the surface area of the larger solid is approximately 125.28 mm^2.