Question

substitute the given values into the given formula and solve for the unknown variable. if necessary, round to one decimal place.

$v = \frac{1}{3}\pi r^{2}h; v = 1138.8, \pi = 3.14, r = 8$ (volume of a cone)

Explanation:

Step1: Substitute given values into formula

Substitute $V = 1138.8$, $\pi=3.14$, and $r = 8$ into $V=\frac{1}{3}\pi r^{2}h$. We get $1138.8=\frac{1}{3}\times3.14\times8^{2}\times h$.

Step2: Simplify the right - hand side

First, calculate $8^{2}=64$. Then $\frac{1}{3}\times3.14\times64\times h=\frac{3.14\times64}{3}h=\frac{200.96}{3}h$.

Step3: Solve for h

We have the equation $1138.8=\frac{200.96}{3}h$. Multiply both sides by 3 to get $1138.8\times3 = 200.96h$, so $3416.4=200.96h$. Then $h=\frac{3416.4}{200.96}\approx17.0$.

Answer:

$h\approx17.0$