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Math Help - Alittle help here please

  1. #1
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    Alittle help here please

    I am trying to get a formula for the lateral surface area of 2 semi circles that is a right solid that have a height of 14 meters. The small semi circle has a radius of 15 and the large semi circle has a radius of 18 and there is a middle length of 23, these are connected in the middle and it is kinda hard to explain but think of a orange that is smaller on one half then the other.My teacher loves this problem but he has yet to produce the formula for it. I am flustered here.
    Am I making any sense?
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by msgoth View Post
    I am trying to get a formula for the lateral surface area of 2 semi circles that is a right solid that have a height of 14 meters. The small semi circle has a radius of 15 and the large semi circle has a radius of 18 and there is a middle length of 23, these are connected in the middle and it is kinda hard to explain but think of a orange that is smaller on one half then the other.My teacher loves this problem but he has yet to produce the formula for it. I am flustered here.
    Am I making any sense?
    Not to me. Sorry.

    -Dan
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  3. #3
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    Quote Originally Posted by msgoth View Post
    I am trying to get a formula for the lateral surface area of 2 semi circles that is a right solid that have a height of 14 meters. The small semi circle has a radius of 15 and the large semi circle has a radius of 18 and there is a middle length of 23, these are connected in the middle and it is kinda hard to explain but think of a orange that is smaller on one half then the other.My teacher loves this problem but he has yet to produce the formula for it. I am flustered here.
    Am I making any sense?
    Hello,

    I've attached a sketch of a solid and I hope I got your description right

    According to the measures you gave the surface area consists of:
    1 large circle + 1 large curved surface area + 1 small circle + 1 small curved surface area + 1 large rectangle - 1 small rectangle:

    Let R, H be the radius and height of the large cylinder and
    r, h the radius and height of the small cylinder then you formula is:

    a_{surface} = \pi \left(R(R+H) +r(r+h)\right)+(R \cdot H-r \cdot h)

    With your numbers you get:

    \pi \cdot 18^2 + \pi \cdot 18 \cdot 23 + \pi \cdot 15^2 + \pi \cdot 15 \cdot 14 + (18 \cdot 23-15 \cdot 14) = 1173 \cdot \pi+204 \approx 3889.088~m^2
    Attached Thumbnails Attached Thumbnails Alittle help here please-zweihalbezylinder.jpg  
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