Question

The volume V of a cone varies jointly as the square of the radius of the base,r, and the height, h. Find the equation of the joint variation if v =285, r=4, and h = 17.

Answer 1

Answer:

V = 1.05r²h

Explanation:

The expression ''the volume V of a cone varies jointly as the square of the radius of the base,r, and the height, h'' can be represented as:

$V=k\cdot r^2\cdot h$

Where the k is a constant.

So, replacing V = 285, r = 4, and h = 17, we get:

$285=k\cdot4^2\cdot17$

Solving for k, we get:

$\begin{gathered} 285=k\cdot16\cdot17 \\ 285=k\cdot272 \\ \frac{285}{272}=\frac{k\cdot272}{272} \\ 1.05=k \end{gathered}$

So, the equation of the joint variation is:

$V=1.05r^2h$