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# The base diameter of a right circular cone is 18 cm. If the lateral area is 516.4 cm2, find its volume in cubic centimeters

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The base diameter of a right circular cone is 18 cm. If the lateral area is 516.4 cm2, find its volume in cubic centimeters
Jan 17, 2020

#1
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The base diameter of a right circular cone is 18 cm. If the lateral area is 516.4 cm2, find its volume in cubic centimeters

Jan 17, 2020
edited by Omi67  Jan 17, 2020
#2
+24422
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The base diameter of a right circular cone is $$18~\text{cm}$$.
If the lateral area is $$516.4~\text{cm}^2$$, find its volume in cubic centimeters

$$\text{Let the radius of the circle  r = 9~\text{cm}  } \\ \text{Let the lateral area  F_\text{lateral} = 516.4~\text{cm}^2 } \\ \text{Let the circle area  F_\text{circle} = \pi r^2 =81\pi= 254.469\ldots~\text{cm}^2 }$$

volume:

$$\begin{array}{|rcll|} \hline \mathbf{V_{\text{circular cone}}} &=& \mathbf{\dfrac{r}{3}*\sqrt{F_\text{lateral}^2 - F_\text{circle}^2}} \\\\ &=& \dfrac{9~\text{cm}}{3}*\sqrt{\left(516.4~\text{cm}^2\right)^2 - \left(254.469\ldots~\text{cm}^2\right)^2} \\\\ &=& 3~\text{cm}*\sqrt{266668.96~\text{cm}^4 - 64,754.4744755~\text{cm}^4} \\ &=& 3~\text{cm}*\sqrt{201,914.485524~\text{cm}^4} \\ &=& 3~\text{cm}*449.348957409~\text{cm}^2 \\ &=& 1348.04687223~\text{cm}^3 \\ \mathbf{ \mathbf{V_{\text{circular cone}}} } &=& \mathbf{1348.0~\text{cm}^3} \\ \hline \end{array}$$

Jan 17, 2020
edited by heureka  Jan 17, 2020