The surface areas of two similar solids are 289 ft2 and 900 ft2. The volume of the larger solid is 1,755 ft3. What is the volume of the smaller solid?
the surface areas of two similar objects are proportional to the square of their sides
small side^2 / large side^2= 900/289
small side/large side = 30/17
volume of two similar objects is proportional to the cubes of their sides
smaller volume/1755 = 17^3/30^3
smaller volume = 1755(4913/27000) = appr 319
289 x 1755/900 = 563.55
To find the relationship between the surface areas and volumes of similar solids, we can use the proportionality principle. This principle states that for similar solids, the ratios of their corresponding lengths, surface areas, and volumes are equal.
In this case, let's assume the surface area of the smaller solid is A1, the surface area of the larger solid is A2, the volume of the smaller solid is V1, and the volume of the larger solid is V2.
Given that A1 = 289 ft², A2 = 900 ft², and V2 = 1,755 ft³, we need to find V1.
Using the proportionality principle, the ratio of the surface areas is equal to the ratio of the volumes:
(A1/A2) = (V1/V2)
Substituting the given values, we have:
(289/900) = (V1/1,755)
To solve for V1, we can cross-multiply and then divide:
289 × 1,755 = 900 × V1
506,895 = 900 × V1
V1 = 506,895/900
V1 ≈ 563.22 ft³
Therefore, the volume of the smaller solid is approximately 563.22 ft³.