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Math Help - pyramid volume with integrals

  1. #1
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    Unhappy pyramid volume with integrals

    1. You wake up one morning, and find yourself wearing a toga and scarab ring. Always a logical person, you conclude that you must have become an Egyptian pharoah. You decide to honor yourself with a pyramid of your own design. You decide it should have height h=830 and a square base with side s=870

    2. Find the volume of the solid formed by rotating the region enclosed by

    x=0 x=1 y=0 y=8+x^4 about the x-axis.

    3. A ball of radius 11 has a round hole of radius 3 drilled through its center. Find the volume of the resulting solid
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  2. #2
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    Quote Originally Posted by ws8211 View Post
    1. You wake up one morning, and find yourself wearing a toga and scarab ring. Always a logical person, you conclude that you must have become an Egyptian pharoah. You decide to honor yourself with a pyramid of your own design. You decide it should have height h=830 and a square base with side s=870
    Wow. So much irrevalant information. What's the question exactly?

    2. Find the volume of the solid formed by rotating the region enclosed by

    x=0 x=1 y=0 y=8+x^4 about the x-axis.
    What you have is basically the area under y = 8 + x^{4} from x = 0 to 1. You can use the washer method to compute the volume:
    V = \pi \int_{0}^{1} \bigg[ f(x) \bigg]^{2} dx \: \: = \: \: \pi \int_{0}^{1} \left(8 + x^{4}\right)^{2} dx


    3. A ball of radius 11 has a round hole of radius 3 drilled through its center. Find the volume of the resulting solid
    Find the volume of the big ball (in its entirety before it was drilled into). Find the volume of the small hole. Subtract.
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  3. #3
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    for No. 1

    thanks for the help

    the question number 1

    To impress your Egyptian subjects, find the volume of the pyramid.

    this is what they want...

    thanks
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    1. V_{\text{pyramid}}= \frac{1}{3}Bh
    where B = area of the base and h = the height
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    No.1

    but i only have a S value.

    i put 1/3 *830*870= 240700

    but the answer was wrong
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    Visualize the pyramid. You have the height already so know worries about that. You have the square base. You are given the length of the square's side. What's the area of the square then?
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  7. #7
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    Quote Originally Posted by ws8211 View Post
    1. You wake up one morning, and find yourself wearing a toga and scarab ring. Always a logical person, you conclude that you must have become an Egyptian pharoah. You decide to honor yourself with a pyramid of your own design. You decide it should have height h=830 and a square base with side s=870
    I actually think this teacher was quite clever, it wakes people up when they see crazy problems like this!
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  8. #8
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    Quote Originally Posted by elizsimca View Post
    I actually think this teacher was quite clever, it wakes people up when they see crazy problems like this!
    Except Egyptian Pharaohs don't (or rather did not) ware togas, they are Roman. Alsa Pharaoh has other more distinctive acoutrements than a scarab ring, perhaps the double crown of upper and lower Egypt on the night stand next to the bed might have been a better clue)

    RonL
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