## eroshea Group Title 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? one year ago one year ago

1. agent0smith Group Title

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

2. eroshea Group Title

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

3. agent0smith Group Title

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 $5 = \frac{ 1 }{ 3 } B \times 2 \sin 65$

4. agent0smith Group Title

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.

5. eroshea Group Title

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

6. agent0smith Group Title

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

7. eroshea Group Title

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

8. agent0smith Group Title

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.

9. eroshea Group Title

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

10. agent0smith Group Title

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

11. eroshea Group Title

thanks :)