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Mensuration Question

Hey guys,

Having difficulty with this question and have had 3 different answers for it and am not sure how!!
A cyclinder cal can contains a liquid that has a capacity of 250 ml. It is filled to leave a gap of 1cm between liquid surface and top of the can. Diameter is 8cm. What is the total capacity of the can (including gap) and how much material is required for each can?

Any help would be great. Thanks :smile:
Reply 1
Avatar for jadys10
jadys10
14
Original post by Pokeyguy20
Hey guys,

Having difficulty with this question and have had 3 different answers for it and am not sure how!!
A cyclinder cal can contains a liquid that has a capacity of 250 ml. It is filled to leave a gap of 1cm between liquid surface and top of the can. Diameter is 8cm. What is the total capacity of the can (including gap) and how much material is required for each can?

Any help would be great. Thanks :smile:


Since
V = 250cm³ (1mL = 1cm³) and d=8cm
This means
r=8/2=4cm

And using
V = πr²h
Rearrange to solve for h (height of liquid)
h=V/πr²
h=250/π*4²
h=250/16π
h=4.97cm (2d.p)

So height of the cylinder would be 4.97cm +1cm=5.97cm
Capacity (V) = 16π*5.97 = 300.08ml = 300ml

Area material that makes up the can (surface area):
Work out the circumference
c=2πr=πd
c=8π

A=c*h or b*h or w*l (however you wanna call it)
Area of the the bit wrapping around the can = 8π*5.97 = 150.04cm²

A=πr²
Total area of the top and bottom circles of the can = π*4²*2 = 32π

Area of material to make up the can= 32π+150.04 = 250.57 = 250.6cm²
Reply 2
Avatar for jadys10
jadys10
14
Can I just say that I'm assuming that the liquid in the can is 250ml, not that 250ml is the full capacity of the can, so in the end I got 300ml as the full capacity of each can and area of material to make up each can to be 250.6cm²
Reply 3
Avatar for Pokeyguy20
Pokeyguy20
OP
1
Original post by jadys10
Can I just say that I'm assuming that the liquid in the can is 250ml, not that 250ml is the full capacity of the can, so in the end I got 300ml as the full capacity of each can and area of material to make up each can to be 250.6cm²


That's great many thanks. That was one of my answers but the question was vague so assumed it was just te liquid that was 250ml. :smile:

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