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- anonymous

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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- anonymous

- jamiebookeater

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- agent0smith

|dw:1355654103593:dw|
Guessing it looks like this...

- anonymous

but it is not a right triangle so i can't use SOH CAH TOA there

- agent0smith

You 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
\[5 = \frac{ 1 }{ 3 } B \times 2 \sin 65\]

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- agent0smith

This 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.

- anonymous

B is 8.28
and B = pi r^2
root 8.28/pi = r ??? is that correct?

- agent0smith

Remember that the question is asking for the area of the base, which is the B. It's not asking for the radius.

- anonymous

yes.. but i'm just asking whether what i did up there is right or wrong..

- agent0smith

I 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.

- anonymous

that's fine.. thanks for helping :))

- agent0smith

If you were asked for the radius, then you'd do as you did:
\[r = \sqrt{\frac{ 8.275 }{ \pi }}\]

- anonymous

thanks :)

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