#### 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.

#### Solution

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

Is there an error in this question or solution?

Solution 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. Concept: Surface Area of a Right Circular Cylinder.