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4 September, 19:50

The surface areas of two similar solids are 340 yd2 and 1,158 yd2. The volume of the larger solid is 1,712 yd3. What is the volume of the smaller solid?

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  1. 4 September, 22:35
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    Let us say that,

    1 = smaller solid

    2 = larger solid

    We must remember that the surface area of an object is proportional to the square of their sides, therefore,

    SA = k s^2

    where k is the constant of proportionality.

    By taking the ratio of the 2 similar solids:

    SA2 / SA1 = k s2^2 / k s1^2

    SA2 / SA1 = s2^2 / s1^2

    sqrt (SA2 / SA1) = s2 / s1

    s2 / s1 = sqrt (1158 / 340)

    While the volume of an object is proportional to the cube of their sides, therefore:

    V = k’ s^3

    where k’ is the constant of proportionality.

    By taking the ratio of the 2 similar solids:

    V2 / V1 = k’ s2^3 / k’ s1^3

    V2 / V1 = s2^3 / s1^3

    1712 / V1 = [sqrt (1158 / 340) ]^3

    1712/V1 = 6.28556705

    V1 = 272.37 yd^3
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