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 $14$ $14$ . If the volume of the solid is $2750 π$ $2750 pi$ , what is the area of the base of the cylinder?

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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 $14$ $14$ . If the volume of the solid is $2750 π$ $2750 pi$ , what is the area of the base of the cylinder?

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Answer 1 · 2016-03-19T16:32:44

$110 π$ $110 pi$ [square units]

Explanation:

$V_{T} = V_{cylinder} + V_{cone}$ $V_T=V_("cylinder")+V_("cone")$
$V_{T} = S_{\circ} \cdot h_{cylinder} + \frac{S_{\circ} \cdot h_{cone}}{3}$ $V_T=S_circ*h_("cylinder")+(S_circ*h_("cone"))/3$
$V_{T} = π \cdot r^{2} \cdot h_{cylinder} + \frac{π \cdot r^{2} \cdot h_{cone}}{3}$ $V_T=pi*r^2*h_("cylinder")+(pi*r^2*h_("cone"))/3$
$π \cdot r^{2} \cdot (h_{cylinder} + \frac{h_{cone}}{3}) = V_{T}$ $pi*r^2*(h_("cylinder")+h_("cone")/3)=V_T$

$π \cdot r^{2} = S_{cylinder's base} = \frac{3 \cdot V_{T}}{3 \cdot h_{cylinder} + h_{cone}} = \frac{3 \cdot 2750 π}{3 \cdot 14 + 33} = \frac{8250 π}{75} = 110 π$ $pi*r^2=S_("cylinder's base")=(3*V_T)/(3*h_("cylinder")+h_("cone"))=(3*2750pi)/(3*14+33)=(8250pi)/75=110pi$ [square units]

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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 $14$ $14$ . If the volume of the solid is $2750 π$ $2750 pi$ , what is the area of the base of the cylinder?

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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 3333 and the height of the cylinder is 1414 . If the volume of the solid is 2750π2750 pi, what is the area of the base of the cylinder?

1 Answer

Explanation:

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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 $14$ $14$ . If the volume of the solid is $2750 π$ $2750 pi$ , what is the area of the base of the cylinder?