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# 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. - CBSE Class 9 - Mathematics

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ConceptSurface Area of a Right Circular Cylinder

#### 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?

#### APPEARS IN

RD Sharma Solution for Mathematics for Class 9 by R D Sharma (2018-19 Session) (2018 to Current)
Chapter 19: Surface Areas and Volume of a Circular Cylinder
Ex.19.10 | Q: 13 | Page no. 8
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.
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