A cylinder has a volume of 300 cubic inches and its height is equal to its radius. The cylinder and a sphere have the same radius. What is the volume of the sphere?
FORMULAS:
Cylinder- 3.14 X r^2 X h
Sphere- 4/3 X 3.14 X r^3

Question

darkknight · Answer

cylinder volume = pi * r^2 * h
plug and chug, $$300=\pi*r^2*h$$
where $$r=h$$ so $300=\pi*r^2*r$ or  $300=\pi*r^3$ so  $300/ \pi =r^3$
and $$r=\sqrt[3]{300/\pi}$$

darkknight · Answer

sphere volume $$V=4/3*\pi*r^3$$
we found r to be $$r=\sqrt[3]{300/\pi}$$
plug and chug
$$V=4/3*\pi*\sqrt[3]{300/\pi}$$
solve for the volume

darkknight · Answer

@rival 
You don't know what you are doing, I do, don't waste any more brain cells over here

luvvdani1516 · Answer

My answer choices are:
A) 1200 cubic inches

B) 400 cubic inches

C) 200 cubic inches

D) 100 cubic inches

And I got the answer 122.799205. So, which answer choice do I pick?

darkknight · Answer

@darkknight wrote:

sphere volume $$V=4/3*\pi*r^3$$ we found r to be $$r=\sqrt[3]{300/\pi}$$ plug and chug $$V=4/3*\pi*\sqrt[3]{300/\pi}$$ solve for the volume

bruh im stupid, I meant we have to cube r, my bad $$V=4/3*\pi*(\sqrt[3]{300/\pi})^3$$

darkknight · Answer

@luvvdani1516 wrote:

My answer choices are: A) 1200 cubic inches B) 400 cubic inches C) 200 cubic inches D) 100 cubic inches And I got the answer 122.799205. So, which answer choice do I pick?

follow all the steps above, I did not get 122 or anywhere near that

luvvdani1516 · Answer

@darkknight wrote:

@luvvdani1516 wrote:

My answer choices are: A) 1200 cubic inches B) 400 cubic inches C) 200 cubic inches D) 100 cubic inches And I got the answer 122.799205. So, which answer choice do I pick?

follow all the steps above, I did not get 122 or anywhere near that

I did and that's what I got.

darkknight · Answer

$$V=4/3*\pi*(\sqrt[3]{300/\pi})^3$$
you plugged this in and got 122?

darkknight · Answer

@luvvdani1516 still there?

luvvdani1516 · Answer

@darkknight wrote:

$$V=4/3*\pi*(\sqrt[3]{300/\pi})^3$$ you plugged this in and got 122?

I keep getting 122. What am I doing wrong? I'm putting everything there into my calculator and I'm still getting the same answer.

darkknight · Answer

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darkknight · Answer

or $$4/3*\pi*300/\pi=4/3*300=400$$ because the cube root and cube cancels

luvvdani1516 · Answer

@darkknight wrote:

I don't understand why I was not getting that answer. But, thanks for the help.

darkknight · Answer

np

surjithayer · Answer

$$r^3=\frac{ 300 }{\pi  }$$
volume of sphere
$$=\frac{ 4 }{ 3 } \pi r^3$$
$$=\frac{ 4 }{ 3 }\pi (\frac{ 300 }{ \pi })$$
=400 cubic inches.

luvvdani1516 · Answer

@surjithayer wrote:

$$r^3=\frac{ 300 }{\pi }$$ volume of sphere $$=\frac{ 4 }{ 3 } \pi r^3$$ $$=\frac{ 4 }{ 3 }\pi (\frac{ 300 }{ \pi })$$ =400 cubic inches.

That's so much easier to understand lol

luvvdani1516 · Answer

Thank you for the help everyone!

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