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eroshea
 3 years ago
The axis of the cone 2m long makes an angle of 65 degrees with its horizontal base. What is the area of the base if its volume is 5 cu. m?
eroshea
 3 years ago
The axis of the cone 2m long makes an angle of 65 degrees with its horizontal base. What is the area of the base if its volume is 5 cu. m?

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agent0smith
 3 years ago
Best ResponseYou've already chosen the best response.1dw:1355654103593:dw Guessing it looks like this...

eroshea
 3 years ago
Best ResponseYou've already chosen the best response.1but it is not a right triangle so i can't use SOH CAH TOA there

agent0smith
 3 years ago
Best ResponseYou've already chosen the best response.1You still can. Notice the height h makes a right angle with the base. dw:1355654861209:dw Volume of a cone is 1/3x(area of base)x(height) or \[V = \frac{ 1 }{ 3 } B h\] B is area of the base, h is height. We can find height from the diagram: \[\sin 65 = \frac{ h }{2 }\] so h=2sin65 and we know V = 5 cm^3 \[5 = \frac{ 1 }{ 3 } B \times 2 \sin 65\]

agent0smith
 3 years ago
Best ResponseYou've already chosen the best response.1This diagram may help: http://upload.wikimedia.org/wikipedia/commons/d/d2/Cone_3d.png notice the cone on the right, h makes a right angle with the base, and we know the angle that the axis makes with the base.

eroshea
 3 years ago
Best ResponseYou've already chosen the best response.1B is 8.28 and B = pi r^2 root 8.28/pi = r ??? is that correct?

agent0smith
 3 years ago
Best ResponseYou've already chosen the best response.1Remember that the question is asking for the area of the base, which is the B. It's not asking for the radius.

eroshea
 3 years ago
Best ResponseYou've already chosen the best response.1yes.. but i'm just asking whether what i did up there is right or wrong..

agent0smith
 3 years ago
Best ResponseYou've already chosen the best response.1I got B as 8.275 m^2, so you're correct. Don't forget the units, metres squared. btw i made a mistake up there, i said V = 5 cm^3 but it's m^3 not cm^3.

eroshea
 3 years ago
Best ResponseYou've already chosen the best response.1that's fine.. thanks for helping :))

agent0smith
 3 years ago
Best ResponseYou've already chosen the best response.1If you were asked for the radius, then you'd do as you did: \[r = \sqrt{\frac{ 8.275 }{ \pi }}\]
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