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Calculus

10th Edition
Ron Larson + 1 other
ISBN: 9781285057095

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BuyFindarrow_forward

Calculus

10th Edition
Ron Larson + 1 other
ISBN: 9781285057095
Textbook Problem

Surface Area A portion of a sphere of radius r is removed by cutting out a circular cone with its vertex at the center of the sphere. The vertex of the cone forms an angle of 2θ. Find the surface area removed from die sphere.

To determine

To calculate: The surface area removed from the sphere when portion of sphere of radius r is removed by cutting out a circular cone with vertex at center of sphere and the vertex of cone forms an angle 2θ.

Explanation

Given:

Portion of sphere of radius r is removed by cutting out a circular cone with vertex at center of sphere and the vertex of cone forms an angle 2θ.

Formula used:

Formula of surfcae area, s=2πabg(φ)(dxdφ)2+(dydφ)2.

Calculation:

The parametric equations are:

x=f(φ)=rcosφ

And

y=g(φ)=rsinφ

Differntiate both functions with respect to φ

dxdφ=rsinφ

And

dydφ=rcosφ

Formula of surfcae area is,

s=2πabg(φ)(dxdφ)2+(dydφ)2

Put all the values in the equation,

s=2

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