Three intersecting solid circular cylinders

Calculus Level 4

Three solid circular cylinders of equal radius 3 cm 3 \text{ cm} are intersecting perpendicularly along x x , y y and z z axes (As shown in the figure below). Find out the volume of solid of intersection in cm 3 \text{cm}^3 .


The answer is 126.5298705.

Harish Chandra Rajpoot by Harish Chandra Rajpoot , 30, India

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1 solution

using double integration in polar coordinates, one can easily deduce the following formula to compute the volume of intersection of three solid cylinders of radius R R

V = 8 ( 2 − 2 ) R 3 V=8(2-\sqrt 2)R^3

setting the value of radius R = 3 c m R=3\ cm one can find the volume of solid of intersection

V = 8 ( 2 − 2 ) ( 3 3 ) ≈ 126.5298705 c m 3 V=8(2-\sqrt2)(3^3)\approx 126.5298705\ cm^3

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