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U is inversely proportional to the cube of V and U = 81 w...

U is inversely proportional to the cube of V and U = 81 when V = 2. Find U when V = 3

A.

24

B.

27

C.

32

D.

36

View answer & explanation

Correct answer is A

U $\propto \frac{1}{V^3}$

U = $\frac{k}{V^3}$

k = UV $^3$

k = 81 x 2 $^3$ = 81 x 8

When V = 3,

U = $\frac{k}{V^3}$

U = $\frac{81 \times 8}{3^3}$

U = $\frac{81 \times 8}{27}$ = 24

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