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
Verified Correct Answer: A.
Step-by-Step Mathematical Solution
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
Source: Myschool Past Questions Archive (Record #27223)