The shape of a solid is a cylinder surmounted by a cone. If the volume of the solid is $40656\space cm^3$, the diameter of the base is $42\space cm$ and the height of the cylinder is $20\space cm$, find the slant height of the conical portion.
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$45\space cm$
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$35\space cm$
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$40\space cm$
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$50\space cm$
B
Correct answer
Explanation
Volume = pi * r^2 * h_cyl + (1/3) * pi * r^2 * h_cone. r = 21, h_cyl = 20. Volume = pi * 21^2 * 20 + (1/3) * pi * 21^2 * h_cone = 40656. Using pi = 22/7, 8820 * 22/7 + 147 * 22/7 * h_cone = 40656. 27720 + 462 * h_cone = 40656. 462 * h_cone = 12936, h_cone = 28. Slant height = sqrt(r^2 + h_cone^2) = sqrt(21^2 + 28^2) = sqrt(441 + 784) = sqrt(1225) = 35.