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# Wanna know if im right with cup volume

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A cup has a base radius of 3cm, a height of 15cm and a top radius of 5cm, calculate the volume

i got 769.69ml, just wanna know if im right or not

Guest Jul 24, 2017
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A cup has a base radius of 3cm,
a height of 15cm and a top radius of 5cm,
calculate the volume
i got 769.69ml, just wanna know if im right or not

Volume cup:  $$V = \frac13 \pi \cdot 5^2 \cdot H - \frac13 \pi \cdot 3^2 \cdot ( H - 15 )$$

Height H of the cone: $$\frac{H-15}{3} = \frac{H}{5}$$

$$\begin{array}{|rcll|} \hline \frac{H-15}{3} &=& \frac{H}{5} \\ 5\cdot(H-15) &=& 3H \\ 5H-75 &=& 3H \\ 2H &=& 75 \\ H &=& \frac{75}{2} \\ \mathbf{H} &\mathbf{=}& \mathbf{37.5} \\\\ H-15 &=& 37.5 - 15 \\ \mathbf{H-15} &\mathbf{=}& \mathbf{22.5} \\ \hline \end{array}$$

$$\begin{array}{|rcll|} \hline V &=& \frac13 \pi \cdot 5^2 \cdot H - \frac13 \pi \cdot 3^2 \cdot ( H - 15 ) \\\\ &=& \frac13 \pi \cdot 5^2 \cdot 37.5 - \frac13 \pi \cdot 3^2 \cdot 22.5 \\\\ &=& \frac13 \pi \cdot ( 5^2 \cdot 37.5 - 3^2 \cdot 22.5 ) \\\\ &=& \frac13 \pi \cdot ( 25 \cdot 37.5 - 9 \cdot 22.5 ) \\\\ &=& \frac13 \pi \cdot ( 937.5 - 202.5 ) \\\\ &=& \frac13 \pi \cdot 735 \\\\ &=& 245 \pi \\ &=& 769.690200129 \ cm^3 \\ \mathbf{V} &\mathbf{=}& \mathbf{769.69\ldots \ ml} \\ \hline \end{array}$$

heureka  Jul 24, 2017

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