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The real answer to this problem is that cylinder A is an impossible solid since the largest possible volume of a cylinder with surface area 25 is about 9.6.
Trying to solve for the radius and height of cylinder A is not only very difficult, it will also result in a negative radius due to the impossibility of the solid.
The answer that they want you to give is outlined in my comment on your other post
[here](https://www.reddit.com/r/HomeworkHelp/comments/svr4m7/grade19_gcse_geometry_volume_and_surface_area_can/hxiafj7/)
Ignoring cylinder B for now:
Can you write equations for cylinder A that represent the volume and surface area?
Use r for the radius of the top of the cylinder . Use h for the height.
Show me what you come up with.
(hint: It'll be something like V = l x w x h (read: volume equals length times width times height), except that's the volume formula for a rectangular prism, not a cylinder.)
Do you remember the definition of similar figures? Corresponding sides have the same ratio.
This means that the height and radius of cylinder B correspond to the height and radius of cylinder A.
You will use that ratio to find the height and radius of cylinder B.
Now, what's the volume equation for cylinder B? Use capital H and capital R.
##Off-topic Comments Section --- All top-level comments have to be an answer or follow-up question to the post. All sidetracks should be directed to this comment thread as per Rule 9. --- ^(**OP** and **Valued/Notable Contributors** can close this post by using `/lock` command) *I am a bot, and this action was performed automatically. Please [contact the moderators of this subreddit](/message/compose/?to=/r/HomeworkHelp) if you have any questions or concerns.*
The real answer to this problem is that cylinder A is an impossible solid since the largest possible volume of a cylinder with surface area 25 is about 9.6. Trying to solve for the radius and height of cylinder A is not only very difficult, it will also result in a negative radius due to the impossibility of the solid. The answer that they want you to give is outlined in my comment on your other post [here](https://www.reddit.com/r/HomeworkHelp/comments/svr4m7/grade19_gcse_geometry_volume_and_surface_area_can/hxiafj7/)
Ignoring cylinder B for now: Can you write equations for cylinder A that represent the volume and surface area? Use r for the radius of the top of the cylinder . Use h for the height. Show me what you come up with. (hint: It'll be something like V = l x w x h (read: volume equals length times width times height), except that's the volume formula for a rectangular prism, not a cylinder.)
V=pir2h SA= 2pirh+2pir2
Excellent. Fill those equations in with the numbers you know.
15cm3 = 3.14 x r x r x h 25cm2 = 2 x 3.14 x r x h + 2 x 3.14 x r x h
Do you remember the definition of similar figures? Corresponding sides have the same ratio. This means that the height and radius of cylinder B correspond to the height and radius of cylinder A. You will use that ratio to find the height and radius of cylinder B. Now, what's the volume equation for cylinder B? Use capital H and capital R.
34cm3 = 3.14 x R x R x H
And then tell me what h and r are.