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Math Help - Please solve these

  1. #1
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    Please solve these

    Q1. By how many % will the s.a of the cube increase if each side is doubled?

    Q2. A circle of radius 7cm is divided into two sectors by cutting 120 degree sector from the centre.The 2 sectors are used to form 2 cones of l=7cm, find the ratio of bigger cone to smaller cone?

    Q3. If a=csa, b=tsa, v=vol then express v in terms of a & b. (for a cuboid)

    Q4. Find 1/[(2^2)-1]+1/[(4^2)-1]+1/[(6^2)-1]......1/[(20^2)-1]

    Show the statements an solutions as well.

    Thanks
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  2. #2
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    Quote Originally Posted by calbae View Post
    Q1. By how many % will the s.a of the cube increase if each side is doubled?

    Q2. A circle of radius 7cm is divided into two sectors by cutting 120 degree sector from the centre.The 2 sectors are used to form 2 cones of l=7cm, find the ratio of bigger cone to smaller cone?

    Q3. If a=csa, b=tsa, v=vol then express v in terms of a & b. (for a cuboid)

    Q4. Find 1/[(2^2)-1]+1/[(4^2)-1]+1/[(6^2)-1]......1/[(20^2)-1]

    Show the statements an solutions as well.

    Thanks
    Q4. I have two hints:

    1. Your sum is equal to \sum_{n=1}^{10} \frac{1}{(2n)^2 - 1}.

    2. \frac{1}{(2n)^2 - 1} = \frac{1}{(2n - 1)(2n+1)} = \frac{1}{2} \, \left( \frac{1}{2n-1} - \frac{1}{2n+1}\right).
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  3. #3
    Super Member angel.white's Avatar
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    Quote Originally Posted by calbae View Post
    Q1. By how many % will the s.a of the cube increase if each side is doubled?
    Well the area of a square is s^2 where s is the length or height.

    And a cube has 6 squares on it's surface, so
    A(s) = 6~s^2

    So if we double the size of our width, height, and length, then we still have a cube, as they are all equal to 2s

    So we can plug this new value for length into our formula:
    A(2s) = 6~(2s)^2

    A(2s) = 6~(4s^2)

    A(2s) = 4~(6s^2)

    And note that our formula earlier was that A(s) = 6~s^2 So we can substitute this value in:
    A(2s) = 4~A(s)

    So we can see that the surface area of a cube with a side of 2s is 4 times larger than the surface area of a cube with a side of s.

    Based on the wording in the question, I think they want you to say "4 is 3 more than 1, so the surface area increases 300%"
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