Mathematics For Machine Technology
Mathematics For Machine Technology
8th Edition
ISBN: 9781337798310
Author: Peterson, John.
Publisher: Cengage Learning,
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Textbook Question
Chapter 64, Problem 1A

In order to make a conical duct a circular sheet of metal is to be cut in the shape of a sector of a circle. It the radius of the sector is 32.5 in. and the arc length of the sector is 264 in., what will be the volume of the cone? Round the answer to 1 decimal place.

Expert Solution & Answer
Check Mark
To determine

The volume of the cone.

Answer to Problem 1A

Weight of the pipe, V=11325.07in3

Explanation of Solution

Given information:

  Radius of the sector (r)=32.5 inArc length of the sector (l)=26.4 in

Calculations:

Volume of the sector is defined as, V=A×l............(1)

   Where ,  A = Area of the sector l = length of the sector And length of the sector is defined as –l=r(θ×π 180 o )Where,θcentral angle of the sectorSubstituting values,26.4=32.5(θ×π 180 o )θ=26.532.546.54o

Hence, the area of the sector: -

  A=πr2×(θ×θ 360 o )A=π ( 32.5 )2( 46.54) 360oA=428.98 in2

  From Eq. (1),V=A×l=(428.98 in2)×(26.4 in)V=11325.07 in3

Conclusion:

The volume of cone is V=11325.07 in3.

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