Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

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?

  • This Question is Closed
  1. agent0smith
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

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

  2. eroshea
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

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

  3. agent0smith
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    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
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    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
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

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

  6. agent0smith
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    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
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

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

  8. agent0smith
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    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
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

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

  10. agent0smith
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

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

  11. eroshea
    • 3 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    thanks :)

  12. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy