# Diect proportion

• Oct 31st 2008, 08:58 PM
helloying
Diect proportion
The price $p of a steel ball is proportional to the cube of its radius x cm It is known that the price is$48 for a teel ball of certain radius R cm. Find the price of a steel ball of radius R/2 cm . Ans is $6. Please explain to me how to solve why is it$6
• Oct 31st 2008, 09:19 PM
Chop Suey
Given:
$p = kr^3$ for some constant k.

$48 = kR^3$

$p = k\left(\frac{R}{2}\right)^3$

Now, let's rearrange the third equation:

$p = k\frac{R^3}{8} \implies 8P = kR^3$

Notice tha $kR^3$ from second equation equals 48, so substitute:

$8p = 48$

$p = ...$