Quantcast

Got Homework?

Connect with other students for help. It's a free community.

  • across
    MIT Grad Student
    Online now
  • laura*
    Helped 1,000 students
    Online now
  • Hero
    College Math Guru
    Online now

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

virtus Group Title

a drinking glass has the shape of a truncated cone. If the internal radii of the base and the top are 3cm and 4cm respectively and the depth is 10cm, find a)by integration its capacity. b) the volume of water if the glass is filled with water to a depth of 5cm

  • 2 years ago
  • 2 years ago

  • This Question is Closed
  1. alexray19 Group Title
    Best Response
    You've already chosen the best response.
    Medals 3

    To find the volume of the cup filled only 5 cm, just change the bounds from 0 and 10 to 0 and 5

    • 2 years ago
  2. virtus Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    THANK YOU SO MUCH ALEXRAY19!

    • 2 years ago
  3. alexray19 Group Title
    Best Response
    You've already chosen the best response.
    Medals 3

    oh, I forgot to distribute that pi at the end, the answer would be 35pi/2

    • 2 years ago
  4. virtus Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    =)

    • 2 years ago
  5. alexray19 Group Title
    Best Response
    You've already chosen the best response.
    Medals 3

    Actually, I messed that up.... R(x) is supposed to be squared

    • 2 years ago
  6. alexray19 Group Title
    Best Response
    You've already chosen the best response.
    Medals 3

    If R(x) is a function to determine the distance from the axis of rotation and the outer edge of the cup, you can determine the volume of the cup using the Disc Method:\[\pi \int\limits_{a}^{b}[R(x)]^{2}dx\] So there are two things you need to determine: What is R(x) and what are the values for a and b (the integration bounds). To determine what R(x) is, imagine flipping the cup horizontally so the x axis runs through the center of the cup and the bottom of the cup is at x=0. The x axis is the axis of rotation, so find an equation to determine the y value of the edge of the cup for a given x|dw:1328438568479:dw| The y intercept is 1.5 and the slope is 0.5/10 or 5/100. That means R(x) is:\[R(x) = \frac{5}{100}x + 1.5\] The bounds, a and b, would be 0 and 10, because you're going from the bottom of the cup (which is at x=0) to the top of the cup (at x=10). Now you can integrate and solve:\[\pi \int\limits\limits\limits_{0}^{10}(\frac{5}{100}x+1.5)^{2}dx = \pi \int\limits\limits\limits_{0}^{10} \left(\frac{x^2}{16}+\frac{3x}{4}+\frac{9}{4}\right)dx = \pi \left[\frac{x^3}{48}+\frac{3x^{2}}{8}+\frac{9x}{4}\right]_{0}^{10}\] \[= \pi\left[\left(\frac{1000}{48} + \frac{300}{8}+\frac{90}{4}\right) - 0\right] = \frac{485}{6} \approx 80.8333 \]

    • 2 years ago
  7. alexray19 Group Title
    Best Response
    You've already chosen the best response.
    Medals 3

    And forgot to distribute the pi again... so it's about 253.945

    • 2 years ago
  8. virtus Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    thank you!!!!!!!

    • 2 years ago
  9. alexray19 Group Title
    Best Response
    You've already chosen the best response.
    Medals 3

    Actually that's wrong too, but I need to get some sleep or I'm just gonna keep messing up. Sorry :P

    • 2 years ago
  10. virtus Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    night night sleep tight so those neurotransmitters will be able to work tomorrow - then you can have another shot at this question thanks for all the help anyways, greatly appreciated!

    • 2 years ago
    • Attachments:

See more questions >>>

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.