Question

A solid cylinder of radius 10 inches is inscribed in a prism with equilateral triangular bases. Find the volume of the portion of the prism that is outside the cylinder if the common height is 100 inches.

Help please... The answer on my book is 20,542 cubic inches...

Thanks a bunch!

Answer 1

@phi
@UnkleRhaukus
@lakeshow25
@thomaster

Answer 2

Volume of prism = 1/2 x Base x Length x Height

Volume of cylinder = heigh x pi x r^2

From attachment:

Base => x / Sin(60) = 10 / sin (30) => x = 10xSin(60) / Sin(3) = 10 x SQRT(3) inches

Times this by 2 as the circle bisects the triangles side at it's midpoint, so the actual base length is 20 x SQRT(3)

Length => y / sin(60) = (10 x SQRT(3))/Sin(30) => y = 30 inches

with radius of 10" and mutual height of 100",

then the volume of prism outside the cylinder is the volume of the prism minus the volume of the cylinder,

so V_p = 1/2 x 30" x 20xSQRT(3) " x 100) = 51961.52 inches

and V_c = 100 x pi x 100 = 1000pi = 31415.92

so the volume outside is 51961.52 - 31415.92 = 20545.59 inches

:)

Answer 3

@samgrace
Thanks...