The surface area of two similar solids are 450 MM squared and 578 MM squared if the volume of the smaller solid is 511 MM cubed find the volume of the larger solid

Similar solids with surface areas S1, S2 and volumes V1, V2.

S ~ r²

V ~ r³ = >

cuberoot (V2/V1) = sqrt (S2/S1)

(V2/V1) ^ (1/3) = (S2/S1) ^ (1/2), raise to power 3 = >

V2/V1 = (S2/S1) ^ (3/2)

V2 = V1 * (S2/S1) ^ (3/2)

V2 = 511 * (578/450) ^ (3/2)

V2 = 743.86

The volume is 744 mm^3