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Math Help - Working out the Volume of a Cone/Hemi-sphere

  1. #1
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    Unhappy Working out the Volume of a Cone/Hemi-sphere

    Hi all,

    I have a Cone and Hemisphere which are attached together which you can probably imagine in your head as you read this.

    Basically, to the side of the hemisphere of the shape, is a height given as 3.5cm... I know this must also be the radius. So I have that out the way, unless someone else states otherwise

    Now the problem is the cone, it has a height of 4.4cm as wrote beside it. This completely made me go

    So here it is summed up, The cone has a height of 4.4cm and the hemisphere a height of 3.5cm... Work out the volume.

    One more question will be to do with Pyramids

    The Great Pyramid of Cheops is a square-based pyramid. The base has sides of 230m and the height is 147m.

    Using the same material, what would be the height be if you give the base sides of 200m?

    Thank you so much to whoever can help me... I really am so tired from doing this homework and I would rather get my Science homework done before 10pm
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  2. #2
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    Ok let's do this:

    The cone has a height of 4.4cm, the radius is 3.5 (same as hemisphere)

    Let's do the cone first:

    So grab the volume formula

    \frac {1}{3} * \pi * r^2*h

    \frac {1}{3} * \pi * 3.5^2 * 4.4

    You do it from there.

    Now do the hemisphere

    Sphere Formula:

     \frac {4}{3} * \pi * r^3

    you need to divide by 2 because it is half of sphere

     \frac {\frac {4}{3} * \pi * r^3}{2}

    substitute radius in:

    \frac {\frac {4}{3} * \pi * 3.5^3}{2}

    You do it from there.

    Then add together and done.



    Second question:

    Square based pyramid: The base has sides of 230m and the height is 147m.

    I'm assuming the "material" is the volume... if I have misunderstood something then please say so...

    Grab the formula:

     \frac {1}{3} *l*w*h

     \frac {1}{3} * 230 * 230 * 147

    =2592100


    So we need 2592100 "material" to build a square based pyramid with base sides of 200m

    Get the formula out again:

    V= \frac {1}{3} *l*w*h

    Substitute:

     2592100 = \frac {1}{3} * 200 * 200 * h

     64.8025 = \frac {1}{3} * h <--- divide 200 two times.

     194.408 = h <---- divide by 1/3 which is multiply by 3.

    There's your height. The pyramid should use the same material.

    Check:

     \frac {1}{3} * 200 * 200 * 194.408

     = 2592099.999999999 <---- basically the same..

    ok that's it.
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  3. #3
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    Quote Originally Posted by jgv115 View Post
    Ok let's do this:

    The cone has a height of 4.4cm, the radius is 3.5 (same as hemisphere)

    Let's do the cone first:

    So grab the volume formula

    \frac {1}{3} * \pi * r^2*h

    \frac {1}{3} * \pi * 3.5^2 * 4.4

    You do it from there.

    Now do the hemisphere

    Sphere Formula:

     \frac {4}{3} * \pi * r^3

    you need to divide by 2 because it is half of sphere

     \frac {\frac {4}{3} * \pi * r^3}{2}

    substitute radius in:

    \frac {\frac {4}{3} * \pi * 3.5^3}{2}

    You do it from there.

    Then add together and done.



    Second question:

    Square based pyramid: The base has sides of 230m and the height is 147m.

    I'm assuming the "material" is the volume... if I have misunderstood something then please say so...

    Grab the formula:

     \frac {1}{3} *l*w*h

     \frac {1}{3} * 230 * 230 * 147

    =2592100


    So we need 2592100 "material" to build a square based pyramid with base sides of 200m

    Get the formula out again:

    V= \frac {1}{3} *l*w*h

    Substitute:

     2592100 = \frac {1}{3} * 200 * 200 * h

     64.8025 = \frac {1}{3} * h <--- divide 200 two times.

     194.408 = h <---- divide by 1/3 which is multiply by 3.

    There's your height. The pyramid should use the same material.

    Check:

     \frac {1}{3} * 200 * 200 * 194.408

     = 2592099.999999999 <---- basically the same..

    ok that's it.

    Thank you so much mate

    You laid it out so clearly and made it obvious what to do... Now hopefully I shouldn't need help next time
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