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The surface areas of two similar figures are given. The volume of the larger figure is given. Find the volume of the smaller figure.

S.A = 522 in^2

S.A = 1450 in^2

V = 2750 in^3

Please help asap, with the work shown! Tyy!

The surface areas of two similar figures are given. The volume of the larger figure-example-1
User Kaikuchn
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1 Answer

5 votes

Answer:

594 (cubic inches)

Explanation:

when dealing with similar shapes, there's formulae to learn:

k = is scale factor

Length of bigger shape = k X length of smaller shape

area of bigger shape = k² X area of smaller shape

volume of bigger shape = k³ X volume of smaller shape

we are given the surface areas.

area of bigger shape = k² X area of smaller shape

1450 = k² X 522

k² = 1450/522

k = √(1450/522)

= 5/3.

volume of bigger shape = k³ X volume of smaller shape

2750 = (5/3)³ X volume of smaller

volume of smaller = 2750/(5/3)³

= 594 (cubic inches)

User GRB
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