Question

The total surface area of a hollow metal cylinder, open at both ends of external radius 8 cm and height 10 cm is 338 p `cm^2`. Taking r to be inner radius, obtain an equation in r and use it to obtain the thickness of the metal in the cylinder.

Answer 1

Given that,
External radius(R) =8cm 
Height (h)= 10cm 
The total surface area of a hollow metal cylinder = 338 IT `cm^2` 
We know that

`2 πRh + 2πrh + 2πR^2 - 2πR^2=338πR.` 

⇒h(R+r) = (R+r) (R-r)=169

⇒10(8+r)+(8+r)(8-r)=169

⇒80+10r+64-`r^2`=169

⇒`x^2` -10r+25=0

⇒r=5

∴R-r=8-5cm=3cm