A solid consists of a cone on top of a cylinder with a radius equal to that of the cone. The height of the cone is $33$ and the height of the cylinder is $13$ . If the volume of the solid is $2750 pi$ , what is the area of the base of the cylinder?

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Answer 1 · 2018-01-10T04:54:18

Base area of the cylinder

$A_(cyl) = pi r^2 = pi (7.73)^2 = color (blue)(24.29)$

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Volume of the solid $V_s = 2750pi$

Height of cone $h = 33$

Height of cylinder $H = 13$

V_(cone) = (1/3)pi r^2h#

$V_(cyl) = pi r^2 H$

V_s #= volume of cylinder + volume of cone

$V_s = pi r^2 H + (1/3) pi r^2 h$

$2750 cancel(pi) = cancel(pi) r^2 (H + h)$

$r^2 = 2750 / (13 + 33) = 59.78$

$r ~~ 7.73$

Base area of the cylinder

$A_(cyl) = pi r^2 = pi (7.73)^2 = color(blue)(24.29)$

A solid consists of a cone on top of a cylinder with a radius equal to that of the cone. The height of the cone is 33 33 and the height of the cylinder is 13 13 . If the volume of the solid is 2750 pi2750 pi, what is the area of the base of the cylinder?