(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

To reduce heat loss, the surface area of a hot-water tank must be kept to a minimum. If such a tank is 125 litters in capacity, and can be approximated by a cylinder in shape with a hemispherical end cap; calculate the radius and overall height for minimum heat loss.

hi can anyone check my ansers please thanks

3. The attempt at a solution

125 litres = 125000 cm^3

The volume is the sum of the volume of a hemisphere and a cylinder.

V= 2/3 πr^3+πr^2 h

The surface area is

S=2πrh+2πr^2

Isolate h in the Volume equation.

V= πr^3+πr^2 h

h=(V- 2/3 πr^2 )/(πr^2 )

Substitute for h into the Surface area equation.

S=2πr^2 (V- 2/3 πr^2 )/(πr^2 )+2πr^2

S=(2V )/r+2/3 πr^2

calculate the derivative.

ds/dr= - (2V )/r^2 +4/3 πr

Solve for r

- 2V + 4/3 πr^3=0

r^3= (3v )/2π

r^3= (3 ×125000 )/2π

r^3= 59683

r= ∛59683

r = 39.1 cm

to calculate the height

h=(125000- 2/3 π〖39.1〗^2 )/(π〖39.1〗^2 )

Height = 25 cm

sorry can figuare how to make the equations non linnear

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# Homework Help: Hot water cylinder

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