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17 May, 02:27

A birthday cake is in the shape of 2 cylinders, one smaller one on top of another larger one. The radius of the bottom layer of cake is (3x  2) and the radius of the top layer of cake is (x  4). The height for each layer is 6 cm. Determine a simplified expression for the difference in volume between the cake layers.

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  1. 17 May, 04:33
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    Answer: 6π (8x^2 + 4x - 12)

    Step-by-step explanation:

    Given that the radius of the bottom layer of cake is (3x + 2) and the radius of the top layer of cake is (x + 4). The height for each layer is 6 cm

    Volume of a cylinder = πr^2h

    Small cylinder

    Volume v = π (x + 4) ^2 * 6

    v = 6π (x^2 + 8x + 16)

    Big cylinder

    Volume V = 6π (3x + 2) ^2

    V = 6π (9x^2 + 12x + 4)

    Expression for the difference in volume between the cake layers will be V - v

    6π (9x^2 + 12x + 4) - 6π (x^2 + 8x + 16)

    6π (8x^2 + 4x - 12)
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