Question

The volume, V, of a cone with EQUAL radius, r, and height, h, is given by: V= pie r^2h/3 . Determine the radius and height of a cone of sand having a volume of 25000 cm^3. Round your answer to the nearest cm.

Answer 1

\[\large V = \pi r^2 \frac{h}{3}\]

We know that r = h ...so we can just make that 'h' another 'r' ...so now we have

\[\large V = \pi r^2 \frac{r}{3}\]

We are given that V = 25000 so plug that in for 'V'

\[\large 25000 = \pi r^2 \frac{r}{3}\]

Alright...now....we have
\[\large 25000 = \frac{\pi r^2 \times r}{3}\]

What is r^2 times r? well r^3 of course...

\[\large 25000 = \frac{\pi r^3}{3}\]

Now we just solve for 'r' can you do that?

Answer 2

yes r= (25000/pie) 1/3

Answer 3

Hmm not quite...

\[\large 25000 = \frac{\pi r^3}{3}\]

The first thing we want to do..is get r^3 by itself....we can do that by multiplying both sides of the equation by 3...because notice...it will eliminate the fraction on the right side

\[\large 75000 = \pi r^3\]

Now..we want to divide both sides by \(\large \pi \) to isolate r^3 completely

\[\large r^3 = \frac{75000}{\pi}\]

Make sense?

Answer 4

ya now i understand sorry lol but how would you put that into your calculator

Answer 5

Well you would look for the \(\large \pi \) symbol

And for NOW...just put 75000 / \(\large \pi\)

Answer 6

so r = 23873.24

Answer 7

Almost...

Remember I just wanted you to focus on the right side of the equation for now....

We actually had \[\large r^3 = \frac{75000}{\pi}\]

We now know that the right side = 23873.24

So

\[\large r^3 = 23873.24\]

Notice that r^3....that means " r cubed " it's like "r squared" but instead of 2 as an exponent....it's 3

Answer 8

That means...to solve this...we need to take the cubed root of both sides of this equation...

\[\huge \sqrt[3]{r^3} = \sqrt[3]{23873.24}\]
\[\huge r = \sqrt[3]{23873.24}\]
\[\large r = ?\]

Answer 9

r= 28.79

Answer 10

Perfect! but remember to round to the nearest cm as the question states...so r = 29 !!

Answer 11

thank you soo much i perfectly understand this now :)

Answer 12

I'm glad :))

Answer 13

:)