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The volume of a frustum of a cone is 1176π cubic meter. If the radius of the lower base is 10 m and the altitude is 18 m. Compute the radius of the upper base.

 Feb 23, 2021
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The volume of a frustum of a cone is 1176π cubic meter. If the radius of the lower base is 10 m and the altitude is 18 m. Compute the radius of the upper base.

 

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\(V=\dfrac{1}{3}\pi h(r_1^2+r_1r_2+r_2^2)\)

\(r_1^2+r_1r_2+r_2^2=\dfrac{3V}{\pi h}\\ r_2(r_2+r_1)=\dfrac{3V}{\pi h}-r_1^2\\ r_2(r_2+10)=\dfrac{3\cdot 1176\pi}{\pi 18}-10^2\\ r_2^2+10r_2-96=0 \)

\(r_2=-5\pm \sqrt{25+96} \)

\(r_2=6m\)

 Feb 23, 2021
edited by asinus  Feb 23, 2021

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