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# Tricky Maths question watch

1. Hey everyone, hope your studyings going well
I'm doing a past paper and I'm stuck on this question so any help would be greatly appreciated.

Question 1:
(In this question, do not substitute a numerical value for pie)
A solid metal cylinder has radius 12cm and height 10cm. The cylinder is melted down and all of the metal made into solid spheres of radius 6cm.
Work out how many of these spheres are made.

Question 2:
An empty box is a cuboid with internal measurements 4cm by 5cm by 10cm. Is it possible to fit a thin. straight rod that is 12cm long entirely inside the box?
2. (Original post by Studystudy)
Hey everyone, hope your studyings going well
I'm doing a past paper and I'm stuck on this question so any help would be greatly appreciated.

Question 1:
(In this question, do not substitute a numerical value for pie)
A solid metal cylinder has radius 12cm and height 10cm. The cylinder is melted down and all of the metal made into solid spheres of radius 6cm.
Work out how many of these spheres are made.

Question 2:
An empty box is a cuboid with internal measurements 4cm by 5cm by 10cm. Is it possible to fit a thin. straight rod that is 12cm long entirely inside the box?
For the first one, work out the volume of the cylinder and the volume of one sphere (leaving your answer in terms of pi) and divide the volume of the cylinder by the volume of the sphere and the answer that you'll get will be the number of spheres that have the same volume as the cylinder.

For the second one, work out the length of the longest diagonal of the box and if this is less than the length of the rod then the rod won't fit.
3. How do I find the diagonals of the box?
4. (Original post by Studystudy)
How do I find the diagonals of the box?
The answer to 1) is 5, btw.

Pythagoras. a² + b² = c²

Then do that again using one diagonal and one side to get the other diagonal.

It works out to a² + b² + c² = d²
5. (Original post by Melanie-v)
The answer to 1) is 5, btw.

Pythagoras. a² + b² = c²

Then do that again using one diagonal and one side to get the other diagonal.

It works out to a² + b² + c² = d²
Yay i got that answer. Ohh ok thanks, i had a feeling but wasn't sure.
6. (Original post by Melanie-v)
The answer to 1) is 5, btw.

Pythagoras. a² + b² = c²

Then do that again using one diagonal and one side to get the other diagonal.

It works out to a² + b² + c² = d²
This is probably just an error in your definitions but I just thought I'd clarify what you've written is incorrect. In order to get the diagonal of the cuboid a x b x c then yes

where d is the length of the diagonal.

However, this c is not the c in

7. I got 5 for the first one, is that right?
8. and for the second i got no, with the diagonal being only 10.31cm?
9. (Original post by MathsLadette)
This is probably just an error in your definitions but I just thought I'd clarify what you've written is incorrect. In order to get the diagonal of the cuboid a x b x c then yes

where d is the length of the diagonal.

However, this c is not the c in

True. I was just giving the standard definitions.

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