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JAMB Mathematics 2011 Paper

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Question : 15

Total: 46

T varies inversely as the cube of R. When R = 3, T =

\frac{2}{81}

, find T when R = 2

$\frac{1}{18}$
$\frac{1}{12}$
$\frac{1}{24}$
$\frac{1}{6}$

Solution:

Concept:

Inverse variation means

T

is proportional to

\frac{1}{R^3}

.

So we write

T = \frac{k}{R^3}

, where

k

is a constant.

Explanation:

Use the given values

R = 3

and

T = \frac{2}{81}

to find

k

.

Substitute into

T = \frac{k}{R^3}

:

\frac{2}{81} = \frac{k}{3^3}

Since

3^3 = 27

, we have:

\frac{2}{81} = \frac{k}{27}

Multiply both sides by

27

:

k = \frac{2}{81} \times 27 = \frac{54}{81} = \frac{2}{3}

Now the formula becomes:

T = \frac{\frac{2}{3}}{R^3}

When

R = 2

, substitute

R^3 = 2^3 = 8

:

T = \frac{\frac{2}{3}}{8} = \frac{2}{3} \times \frac{1}{8} = \frac{2}{24} = \frac{1}{12}

Answer:

T = \frac{1}{12}

This matches option B.

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