# 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. - Mathematics

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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.

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#### 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

Concept: Surface Area of Cylinder
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#### APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 19 Surface Areas and Volume of a Circular Cylinder
Exercise 19.1 | Q 13 | Page 8

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