The-volume-of-a-right-circular-cone-is-5litres-Calculate-the-volume-of-the-part-into-which-the-cone-is-divided-by-a-plane-parallel-to-the-base-one-third-of-the-way-down-from-the-vertex-to-the-base-gi

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Question Number 190634 by Mastermind last updated on 07/Apr/23

$$\mathrm{The}\mathrm{volume}\mathrm{of}\mathrm{a}\mathrm{right}\mathrm{circular}\mathrm{cone}$$$$\mathrm{is}5\mathrm{litres}.\mathrm{Calculate}\mathrm{the}\mathrm{volume}\mathrm{of}$$$$\mathrm{the}\mathrm{part}\mathrm{into}\mathrm{which}\mathrm{the}\mathrm{cone}\mathrm{is}$$$$\mathrm{divided}\mathrm{by}\mathrm{a}\mathrm{plane}\mathrm{parallel}\mathrm{to}\mathrm{the}$$$$\mathrm{base}\mathrm{one}-\mathrm{third}\mathrm{of}\mathrm{the}\mathrm{way}\mathrm{down}$$$$\mathrm{from}\mathrm{the}\mathrm{vertex}\mathrm{to}\mathrm{the}\mathrm{base}\mathrm{giving}$$$$\mathrm{your}\mathrm{answer}\mathrm{to}\mathrm{the}\mathrm{nearest}$$$$\mathrm{millimetres}.$$$$$$$$$$$$\mathrm{Help}!$$

Commented by JDamian last updated on 08/Apr/23

The right cone volume is in litres but the other volume is in milimetres?

Commented by Mastermind last updated on 08/Apr/23

$$\mathrm{Thank}\mathrm{you}\mathrm{but}\mathrm{i}\mathrm{need}\mathrm{full}\mathrm{workings}$$

Commented by Mastermind last updated on 08/Apr/23

$$\mathrm{The}\mathrm{volume}\mathrm{of}\mathrm{a}\mathrm{right}\mathrm{circular}\mathrm{cone}$$$$\mathrm{is}5\mathrm{litres}.\mathrm{Calculate}\mathrm{the}\mathrm{volume}\mathrm{of}$$$$\mathrm{the}\mathrm{part}\mathrm{into}\mathrm{which}\mathrm{the}\mathrm{cone}\mathrm{is}$$$$\mathrm{divided}\mathrm{by}\mathrm{a}\mathrm{plane}\mathrm{parallel}\mathrm{to}\mathrm{the}$$$$\mathrm{base}\mathrm{one}-\mathrm{third}\mathrm{of}\mathrm{the}\mathrm{way}\mathrm{down}$$$$\mathrm{from}\mathrm{the}\mathrm{vertex}\mathrm{to}\mathrm{the}\mathrm{base}\mathrm{giving}$$$$\mathrm{your}\mathrm{answer}\mathrm{to}\mathrm{the}\mathrm{nearest}$$$$\mathrm{millimetres}.$$$$$$$$$$$$\mathrm{I}\mathrm{need}\mathrm{the}\mathrm{full}\mathrm{workings}$$

Commented by mr W last updated on 08/Apr/23

$$whatdoyouexpectasfullworkings?$$$$youhave5litreswaterandyougive$$$$one27thofthewatertoyourfriend.$$$$howmuchwaterdoesheget?$$$$betteryoucheckyourquestionat$$$$first.youcannotgiveyourfriend$$$$somemillimeterswater.thisislike,$$$$wheniask:ifyourfatheris45years$$$$oldandyourageisonethirdofhis,$$$$calculateyourageandgiveyour$$$$answertothenearestkilogram.$$

Commented by mr W last updated on 08/Apr/23

$$inshort:millimeterisnotanunit$$$$forvolume!$$

Commented by mr W last updated on 18/Apr/23

$$youcriedforfullworkingsagain$$$$andagain.butwhensomebodyreally$$$$gaveyouthefullworkings,you$$$${didn}^{\prime }tshowanyreaction.whata$$$$strangehuman!$$

Answered by mr W last updated on 08/Apr/23

Commented by mr W last updated on 08/Apr/23

$$h_1=\frac{h}{3}$$$$\Rightarrow r_1=\frac{r}{3}$$$$V_1=\frac{\pi r_1^2{h}_1}{3}$$$$V=\frac{\pi r^{2}h}{3}$$$$\frac{V_1}{V}={\left(\frac{r_1}{r}\right)}^2\left(\frac{h_1}{h}\right)={\left(\frac{1}{3}\right)}^2=\frac{1}{27}$$$$\Rightarrow V_1=\frac{V}{27}=\frac{5l}{27}=\frac{5\times {10}^6}{27}\approx 185185{mm}^3$$

Commented by Mastermind last updated on 26/Apr/23

$$\mathrm{Thank}\mathrm{you}\mathrm{so}\mathrm{much}$$

Answered by talminator2856792 last updated on 09/Apr/23

$$\mathrm{the}\mathrm{volume}\mathrm{will}\mathrm{be}\frac{5}{27}\mathrm{litres}.$$

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