Question

The volume of this cone is 65.94 cubic feet. What is the radius of this cone? Use ​ ≈ 3.14 and round your answer to the nearest hundredth.

Answer 1

Answer:

In terms of h

radius = 3√7)√ h

Step-by-step explanation:

$volume \: = 65.94 \\ \pi = 3.14 \\ radius =$

$v = \frac{1}{3} \pi {r}^{2} h \\ 65.94 = \frac{1}{3} \times 3.14 \times {r}^{2} \times h \\ 65.94 \times 3 = 1 \times 3.14 \times {r}^{2} h$

$197.82 = 3.14 {r}^{2} h \\ divide \: both \: sides \: of \: the \: equation \: \\ by3.14 h\\ \frac{197.82}{3.14h} = \frac{3.14 {r}^{2}h }{3.14h}$

$\frac{63}{h} = {r}^{2} \\ square \: root \: both \: sides \\ \sqrt{ \frac{63}{h} } = \sqrt{ {r}^{2} } \\ r \: = \frac{3 \sqrt{7} }{ \sqrt{h} }$

Answer 2

Answer:

In terms of h, the radius of the cone is $\frac{3\sqrt{7} }{\sqrt{h} }$

Step-by-step explanation:

The formula for finding the volume of a cone is

$Volume(V) = \frac{1}{3} \pi r^{2} h$

Make r the subject of formula in the equation above

$3V = \pi r^{2} h$

$\frac{3V}{\pi h } = \frac{\pi r^{2} h}{\pi h}$

$r^{2} = \frac{3V}{\pi h}$

Take the square root of both sides of the equation

$\sqrt{r^{2} } = \sqrt{\frac{3V}{\pi h} }$

$r = \sqrt{\frac{3V}{\pi h} }$

Putting in the values given,

$r = \sqrt{\frac{3 * 65.94 }{3.14h} }$

$r = \sqrt{\frac{3 * 21 }{h}}$

$r = \sqrt{\frac{63 }{h} }$

$r = \sqrt{\frac{9 * 7}{h} }$

$r = \frac{3\sqrt{7} }{\sqrt{h} }$

Hope this helps :))