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)
• 68 mam?
• 216 mm?
• 147 mm?
• 16 mm?
216 mm²
Explanation:
Since the two solids are similar, the ratio of their volumes will be the cube of the ratio of their corresponding side lengths.
Let the volume of the larger solid be V and the volume of the smaller solid be V'. Let the surface area of the larger solid be S and the surface area of the smaller solid be S'.
Given:
V/V' = 857.5/540
V/V' = 1.587
Let x be the ratio of the side lengths of the two similar solids.
x^3 = 1.587
Taking the cube root of both sides, we get:
x ≈ 1.17
Since surface area is proportional to the square of the side length, then the surface area of the larger solid will be:
S = (x^2) * S'
S = (1.17^2) * 108
S ≈ 1.37 * 108
S ≈ 147 mm²
Therefore, the surface area of the larger solid is 147 mm².