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Question Number 190634 by Mastermind last updated on 07/Apr/23
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 giving your answer to the nearest millimetres. Help!
$$\mathrm{The}\:\mathrm{volume}\:\mathrm{of}\:\mathrm{a}\:\mathrm{right}\:\mathrm{circular}\:\mathrm{cone} \\ $$$$\mathrm{is}\:\mathrm{5litres}.\:\mathrm{Calculate}\:\mathrm{the}\:\mathrm{volume}\:\mathrm{of} \\ $$$$\mathrm{the}\:\mathrm{part}\:\mathrm{into}\:\mathrm{which}\:\mathrm{the}\:\mathrm{cone}\:\mathrm{is} \\ $$$$\mathrm{divided}\:\mathrm{by}\:\mathrm{a}\:\mathrm{plane}\:\mathrm{parallel}\:\mathrm{to}\:\mathrm{the} \\ $$$$\mathrm{base}\:\mathrm{one}−\mathrm{third}\:\mathrm{of}\:\mathrm{the}\:\mathrm{way}\:\mathrm{down} \\ $$$$\mathrm{from}\:\mathrm{the}\:\mathrm{vertex}\:\mathrm{to}\:\mathrm{the}\:\mathrm{base}\:\mathrm{giving} \\ $$$$\mathrm{your}\:\mathrm{answer}\:\mathrm{to}\:\mathrm{the}\:\mathrm{nearest}\: \\ $$$$\mathrm{millimetres}. \\ $$$$ \\ $$$$ \\ $$$$\mathrm{Help}! \\ $$
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
Thank you but i need full workings
$$\mathrm{Thank}\:\mathrm{you}\:\mathrm{but}\:\mathrm{i}\:\mathrm{need}\:\mathrm{full}\:\mathrm{workings} \\ $$
Commented by Mastermind last updated on 08/Apr/23
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 giving your answer to the nearest millimetres. I need the full workings
$$\mathrm{The}\:\mathrm{volume}\:\mathrm{of}\:\mathrm{a}\:\mathrm{right}\:\mathrm{circular}\:\mathrm{cone} \\ $$$$\mathrm{is}\:\mathrm{5litres}.\:\mathrm{Calculate}\:\mathrm{the}\:\mathrm{volume}\:\mathrm{of} \\ $$$$\mathrm{the}\:\mathrm{part}\:\mathrm{into}\:\mathrm{which}\:\mathrm{the}\:\mathrm{cone}\:\mathrm{is} \\ $$$$\mathrm{divided}\:\mathrm{by}\:\mathrm{a}\:\mathrm{plane}\:\mathrm{parallel}\:\mathrm{to}\:\mathrm{the} \\ $$$$\mathrm{base}\:\mathrm{one}−\mathrm{third}\:\mathrm{of}\:\mathrm{the}\:\mathrm{way}\:\mathrm{down} \\ $$$$\mathrm{from}\:\mathrm{the}\:\mathrm{vertex}\:\mathrm{to}\:\mathrm{the}\:\mathrm{base}\:\mathrm{giving} \\ $$$$\mathrm{your}\:\mathrm{answer}\:\mathrm{to}\:\mathrm{the}\:\mathrm{nearest}\: \\ $$$$\mathrm{millimetres}. \\ $$$$ \\ $$$$ \\ $$$$\mathrm{I}\:\mathrm{need}\:\mathrm{the}\:\mathrm{full}\:\mathrm{workings} \\ $$
Commented by mr W last updated on 08/Apr/23
what do you expect as full workings? you have 5 litres water and you give one 27th of the water to your friend. how much water does he get? better you check your question at first. you can not give your friend some millimeters water. this is like, when i ask: if your father is 45 years old and your age is one third of his, calculate your age and give your answer to the nearest kilogram.
$${what}\:{do}\:{you}\:{expect}\:{as}\:{full}\:{workings}? \\ $$$${you}\:{have}\:\mathrm{5}\:{litres}\:{water}\:{and}\:{you}\:{give} \\ $$$${one}\:\mathrm{27}{th}\:{of}\:{the}\:{water}\:{to}\:{your}\:{friend}. \\ $$$${how}\:{much}\:{water}\:{does}\:{he}\:{get}? \\ $$$${better}\:{you}\:{check}\:{your}\:{question}\:{at} \\ $$$${first}.\:\:{you}\:{can}\:{not}\:{give}\:{your}\:{friend} \\ $$$${some}\:{millimeters}\:{water}.\:{this}\:{is}\:{like}, \\ $$$${when}\:{i}\:{ask}:\:{if}\:{your}\:{father}\:{is}\:\mathrm{45}\:{years} \\ $$$${old}\:{and}\:{your}\:{age}\:{is}\:{one}\:{third}\:{of}\:{his}, \\ $$$${calculate}\:{your}\:{age}\:{and}\:{give}\:{your} \\ $$$${answer}\:{to}\:{the}\:{nearest}\:{kilogram}. \\ $$
Commented by mr W last updated on 08/Apr/23
in short: millimeter is not an unit for volume!
$${in}\:{short}:\:{millimeter}\:{is}\:{not}\:{an}\:{unit} \\ $$$${for}\:{volume}! \\ $$
Commented by mr W last updated on 18/Apr/23
you cried for full workings again and again. but when somebody really gave you the full workings, you didn′t show any reaction. what a strange human!
$${you}\:{cried}\:{for}\:{full}\:{workings}\:{again} \\ $$$${and}\:{again}.\:{but}\:{when}\:{somebody}\:{really} \\ $$$${gave}\:{you}\:{the}\:{full}\:{workings},\:{you}\: \\ $$$${didn}'{t}\:{show}\:{any}\:{reaction}.\:\:{what}\:{a} \\ $$$${strange}\:{human}! \\ $$
Answered by mr W last updated on 08/Apr/23
Commented by mr W last updated on 08/Apr/23
h_1 =(h/3) ⇒r_1 =(r/3) V_1 =((πr_1 ^2 h_1 )/3) V=((πr^2 h)/3) (V_1 /V)=((r_1 /r))^2 ((h_1 /h))=((1/3))^2 =(1/(27)) ⇒V_1 =(V/(27))=((5 l)/(27))=((5×10^6 )/(27))≈185 185 mm^3
$${h}_{\mathrm{1}} =\frac{{h}}{\mathrm{3}} \\ $$$$\Rightarrow{r}_{\mathrm{1}} =\frac{{r}}{\mathrm{3}} \\ $$$${V}_{\mathrm{1}} =\frac{\pi{r}_{\mathrm{1}} ^{\mathrm{2}} {h}_{\mathrm{1}} }{\mathrm{3}} \\ $$$${V}=\frac{\pi{r}^{\mathrm{2}} {h}}{\mathrm{3}} \\ $$$$\frac{{V}_{\mathrm{1}} }{{V}}=\left(\frac{{r}_{\mathrm{1}} }{{r}}\right)^{\mathrm{2}} \left(\frac{{h}_{\mathrm{1}} }{{h}}\right)=\left(\frac{\mathrm{1}}{\mathrm{3}}\right)^{\mathrm{2}} =\frac{\mathrm{1}}{\mathrm{27}} \\ $$$$\Rightarrow{V}_{\mathrm{1}} =\frac{{V}}{\mathrm{27}}=\frac{\mathrm{5}\:{l}}{\mathrm{27}}=\frac{\mathrm{5}×\mathrm{10}^{\mathrm{6}} }{\mathrm{27}}\approx\mathrm{185}\:\mathrm{185}\:{mm}^{\mathrm{3}} \\ $$
Commented by Mastermind last updated on 26/Apr/23
Thank you so much
$$\mathrm{Thank}\:\mathrm{you}\:\mathrm{so}\:\mathrm{much} \\ $$
Answered by talminator2856792 last updated on 09/Apr/23
the volume will be (5/(27)) litres.
$$\:\:\mathrm{the}\:\mathrm{volume}\:\mathrm{will}\:\mathrm{be}\:\frac{\mathrm{5}}{\mathrm{27}}\:\mathrm{litres}.\:\: \\ $$

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