Mass proportion question... confuzzled!?

Question

An open cylindrical container made from sheet metal of uniform thickness has a mass of
800 g. When completely filled with water the total mass is 15.6 kg.

What would be the total mass of a cylindrical container full of water made from the same sheet metal (of the same thickness) but with double the diameter and double the height?

A 118.4 kg
B 121.6 kg
C 124.8 kg
D 128 kg
E 131.2 kg

Please provide working... i did 15.6/0.8 to get 19.5 but then i get stuck.. any help would be greatly appreciated!

Thanks, Ellie x

Answer 1

first look at the cylinder. you're not given the radius or height, but they are not needed to solve anyway.

a cylinder of h height, and r radius weight x pounds
or h*r proportional to x

area of an open ended cylinder equation: pi*r^2 + 2*pi*r*h

if radius and height double, new equation loks like:
pi*(2r)^2 + 2*pi*2r*2h = 4(pi*r^2) + 4(2*pi*r*h)
or
4(pi*r^2 + 2*pi*r*h) => your sureface area quadrupled, so did the mass of the cylinder (4*800g = 3.2kg)

now look at the volume of water, or more appropriately, the volume of the cylinder

V = pi*r^2*h

if radius and height doubled,

V = pi*(2r)^2*2h = 8*pi*r^2*h or volume is 8x bigger.

mass of water = 15.6 kg - 800g = 14.8 kg

14.8*8 = 118.4 kg

add the two together: 118.4+3.2 = 121.6 kg

answer is b)

PS: the guy above me is wrong

Answer 2

The volume of a cylinder equals the (area of the base)*height = ¶r2h
if you double the diameter and you double the height, you are multiplying the volume by 4 (2*2)

If you have a volume that is 4x as big as the original, then the total mass would also be multiplied by 4

15.6 kilograms * 4 = 62.4 kilograms

Answer 3

Ellie,
Go for B and this is why

First area A
A= piR^2 + 2piRH (open top)

A2/A1 =pi(R2^2 + 2R2H2)/pi(R1^2 + 2R1H1)
since H2=2H1 and R2=2R1
Let R1=R and H1=H we have

A2/A1 =4 (R^2 + 2R H)/(R^2 + 2RH)=4
so it will weigh 4 times as much = 3200gm

next and similarly
V=piR^2H
V2/V1=piR2^2 H2/(piR1^2 H1)

V2/V1=8R^2 H/(R^2 H)=8
So it will hold 8 times the volume of water= (15.6 -0.8)8=118.4

Total = 118.4 + 3.20=121.6kg

PS. The second guy above me is correct :-)

Have fun!