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    a solid wooden block. The block is a right prism with length hcm. The
    cross-section of the block is a semi-circle with radius rcm.
    The total surface area of the block, including the curved surface, the two semi-circular
    ends and the rectangular base, is 200cm2
    (a) Show that the volume Vcm3 of the block is given by
    V=πr(200-πr^2)/4+2π
    (b) Use calculus to find the maximum value of V. Give your answer to the nearest cm3.

    (c) Justify, by further differentiation, that the value of V that you have found is a
    maximum.
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    (Original post by sarah5)
    a solid wooden block. The block is a right prism with length hcm. The
    cross-section of the block is a semi-circle with radius rcm.
    The total surface area of the block, including the curved surface, the two semi-circular
    ends and the rectangular base, is 200cm2
    (a) Show that the volume Vcm3 of the block is given by
    V=πr(200-πr^2)/4+2π
    (b) Use calculus to find the maximum value of V. Give your answer to the nearest cm3.

    (c) Justify, by further differentiation, that the value of V that you have found is a
    maximum.
    What are your workings?

    HINT for problems like this one, you generally have to start with the information provided about area and then make a substitution in the volume formula. So what is the formula for the area of the prism?
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    (Original post by BrasenoseAdm)
    What are your workings?

    HINT for problems like this one, you generally have to start with the information provided about area and then make a substitution in the volume formula. So what is the formula for the area of the prism?
    i know that but i don't know the formula of the area and the volume of this cylinder !!
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    (Original post by sarah5)
    i know that but i don't know the formula of the area and the volume of this cylinder !!
    OK

    If it was a cylinder, then area would be

    2πrh+2πr2

    But it seems the shape has a semi-circle base (the question goes on about a right sided prism which is a fancy way of describing a cylinder cut down the middle, right?)



    Can you see what the area is now?
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    (Original post by BrasenoseAdm)
    OK

    If it was a cylinder, then area would be

    2πrh+2πr2

    But it seems the shape has a semi-circle base (the question goes on about a right sided prism which is a fancy way of describing a cylinder cut down the middle, right?)



    Can you see what the area is now?
    Ohhh yess thank you so much
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    (Original post by sarah5)
    Ohhh yess thank you so much
    Great!

    πr^2 + πrh + 2rh

    We are off home now - enjoy your evening.
 
 
 
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