The-volume-of-a-right-circular-cone-is-5-litres-Calculate-the-volumes-of-the-two-parts-into-which-the-cone-is-divided-by-a-plane-parallel-to-the-base-One-third-of-the-way-down-from-the-vertex-to-t

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Question Number 13706 by tawa tawa last updated on 22/May/17

$$\mathrm{The}\mathrm{volume}\mathrm{of}\mathrm{a}\mathrm{right}\mathrm{circular}\mathrm{cone}\mathrm{is}5\mathrm{litres}.\mathrm{Calculate}\mathrm{the}\mathrm{volumes}\mathrm{of}\mathrm{the}\mathrm{two}$$$$\mathrm{parts}\mathrm{into}\mathrm{which}\mathrm{the}\mathrm{cone}\mathrm{is}\mathrm{divided}\mathrm{by}\mathrm{a}\mathrm{plane}\mathrm{parallel}\mathrm{to}\mathrm{the}\mathrm{base},\mathrm{One}\mathrm{third}$$$$\mathrm{of}\mathrm{the}\mathrm{way}\mathrm{down}\mathrm{from}\mathrm{the}\mathrm{vertex}\mathrm{to}\mathrm{the}\mathrm{base}.\mathrm{Give}\mathrm{your}\mathrm{answer}\mathrm{to}\mathrm{the}\mathrm{nearest}$$$$\mathrm{ml}.$$

Answered by ajfour last updated on 22/May/17

$$\frac{V_1}{V_1+V_2}=\frac{\frac{1}{3}\pi r^{2}h}{\frac{1}{3}\pi R^{2}H}={\left(\frac{r}{R}\right)}^2\left(\frac{h}{H}\right)$$$$because\frac{r}{R}=\frac{h}{H}=\frac{1}{3}wehave,$$$$with{V}_1+V_2=5litres$$$$V_1=\frac{V_1+V_2}{27}=\frac{5}{27}litres$$$$=\frac{5000}{27}ml=\frac{555.55}{3}ml$$$$=185ml$$$$V_2=5litre-185ml$$$$=4litre815ml.$$

Commented by tawa tawa last updated on 22/May/17

$$\mathrm{God}\mathrm{bless}\mathrm{you}\mathrm{sir}.$$

Commented by RasheedSindhi last updated on 22/May/17

$$\mathcal{N}ice!$$

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