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Standard IX

Mathematics

Surface Area of a Cylinder

The total sur...

Question

The total surface area of hollow cylinder having the inner and outer radii as $\frac{R}{2}$ and $R$ is $x π R (R + \frac{L}{4})$ . Find x.
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Solution

The correct option is A 3
$CSA of hollow cylinder = 2 π (r_{2} + r_{1}) L = 2 π (\frac{R}{2} + R) L = 3 π R L Bottom and Top faces of hollow cylinder = π (r_{2}^{2} - r_{1}^{2}) = π (R^{2} - (\frac{R}{2})^{2}) = \frac{3}{4} π R^{2} TSA of hollow cylinder = CSA of hollow cylinder + Bottom and Top faces of hollow cylinder = 3 π R L + \frac{3}{4} π R^{2} = 3 π R (R + \frac{L}{4})$

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The total surface area of hollow cylinder having the inner and outer radii as R2 and R is xπR(R+L4). Find x.3

The correct option is A 3CSA of hollow cylinder =2π(r2+r1)L =2π(R2+R)L =3πRLBottom and Top faces of hollow cylinder =π(r22−r21) =π(R2−(R2)2) =34πR2TSA of hollow cylinder = CSA of hollow cylinder + Bottom and Top faces of hollow cylinder =3πRL+34πR2=3πR(R+L4)

The total surface area of hollow cylinder having the inner and outer radii as $\frac{R}{2}$ and $R$ is $x π R (R + \frac{L}{4})$ . Find x.
3