Word problem: A cylinder has the same radius as that of a sphere, which is R cm.

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BanaMath

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A cylinder has the same radius as that of a sphere, which is R cm.
The sim of the volume of th cylinder and the volume of the sphere is 9πR^3 cm^3.
How many times greater is the height of the cylinder than its radius?

I know I've gone wrong somewhere haha..
 

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BanaMath said:
A cylinder has the same radius as that of a sphere, which is R cm.
The sum of the volume of the cylinder and the volume of the sphere is 9πR^3 cm^3.
How many times greater is the height of the cylinder than its radius?

I know I've gone wrong somewhere haha..
Click to expand...

The image is too small to read well, even after enlarging:

1694479557790.png​

It's hard to follow your work, and there seems to be a typo or two along the way. But it looks like you got h = 23R/3. Why do you think that's wrong?
 
BanaMath said:
A cylinder has the same radius as that of a sphere, which is R cm.
The sim of the volume of th cylinder and the volume of the sphere is 9πR^3 cm^3.
How many times greater is the height of the cylinder than its radius?

I know I've gone wrong somewhere haha..
Click to expand...
Please post a higher resolution image - can't read anything.
 
Dr.Peterson said:
The image is too small to read well, even after enlarging:


It's hard to follow your work, and there seems to be a typo or two along the way. But it looks like you got h = 23R/3. Why do you think that's wrong?
Click to expand...
I mean I don't know how to go on to solve the rest of the equation. It asks for How many times greater is the height of the cylinder than its radius?
 
Hopefully this photo is better
 

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BanaMath said:
I mean I don't know how to go on to solve the rest of the equation. It asks for How many times greater is the height of the cylinder than its radius?
Click to expand...
If you have quantities A and B, how do you determine how many times one is greater than the other?
 
You need to figure it out yourself. Just take two numbers and figure out how many one number is greater than the other.
Try 5 and 10. Clearly 10 is 2 times as large as 5. Now, how do you get 2 from 5 and 10?
 
Steven G said:
You need to figure it out yourself. Just take two numbers and figure out how many one number is greater than the other.
Try 5 and 10. Clearly 10 is 2 times as large as 5. Now, how do you get 2 from 5 and 10?
Click to expand...
The ratio between 5:10 is 1:2, you just simplify. So you do that for equations too, thanks!
 
Steven G said:
You need to figure it out yourself. Just take two numbers and figure out how many one number is greater than the other.
Try 5 and 10. Clearly 10 is 2 times as large as 5. Now, how do you get 2 from 5 and 10?
Click to expand...
So is my working out correct so far though?
 

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BanaMath said:
I mean I don't know how to go on to solve the rest of the equation. It asks for How many times greater is the height of the cylinder than its radius?
Click to expand...
You found, correctly, that H = 23R/3. That means H is 23/3 times R. That answers the question, unless you want to write it as a mixed number or decimal. There's no trick to this (that I know of), so I'm not sure why people are making it sound hard. (You did the hard part.)

There's also the little issue that to some people, "5 times greater" means 6 times as much (that is, 5 times as much, added to the original amount), while to others it means 5 times as much. I'd ignore that issue unless somebody mentioned it.
 
Dr.Peterson said:
You found, correctly, that H = 23R/3. That means H is 23/3 times R. That answers the question, unless you want to write it as a mixed number or decimal. There's no trick to this (that I know of), so I'm not sure why people are making it sound hard. (You did the hard part.)

There's also the little issue that to some people, "5 times greater" means 6 times as much (that is, 5 times as much, added to the original amount), while to others it means 5 times as much. I'd ignore that issue unless somebody mentioned it.
Click to expand...
Oh ok, thanks!
 
For the record, @lev888 is right when he said to compare the quantities. Personally, when I want to find out how many times larger 10 is than 5 I compare the numbers by dividing them.
 
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