Mathematics

Question

The formula s= square root of SA/6 gives the length of the side, s, of a cube with a surface area, SA. How much longer is the side of a cube with a surface area of 480 square meters than a cube with the surface area of 270 square meters?

2 Answer

  • Answer: 35 meters


    Step-by-step explanation:

    Given formula s= square root of SA/6 , where s is the side of square

    Surface area of first cube= 480 square meters

    Then side of first cube= [tex]\frac{480}{6}=80\ meters[/tex]

    Now, Surface area of second cube= 270 square meters

    Then side of second cube= [tex]\frac{270}{6}=45\ meters[/tex]

    Difference between their sides=80-45=35 meters

    Hence the side of cube with surface area of 480 square meters is 35 meters longer than the cube with the surface area of 270 square meters

  • Surface area of cube is square of its side length. The side of cube with surface area 480 sq. meters is  0.91 meters longer than the side of cube with 270 sq. meters surface area.


    How to form mathematical expression from the given description?

    You can represent the unknown amounts by the use of variables. Follow whatever the description is and convert it one by one mathematically. For example if it is asked to increase some item by 4 , then you can add 4 in that item to increase it by 4. If something is for example, doubled, then you can multiply that thing by 2 and so on methods can be used to convert description to mathematical expressions.

    For the given case, the phrase "how much longer" denotes that we can use subtraction.

    Let the first cube be A with surface area 480 sq. meters and side p meters

    Then we have

    √(480)/6 = p

    p = √480/6 ≈ 3.65 meters (we took positive root since 'length' is a non-negative quantity)

    Let the second cube be B with surface area 270 sq. meters and side q meters

    Then we have

    √(270)/6 = q

    q ≈ 2.74 meters

    We have: p-q = 3.65 - 2.74 = 0.91 meters approx.

    It means, if we add 0.91 meters to cube B's side length, then its side length would become equal to that of cube A's side length.

    Or, side length of A = 0.91 + side length of B

    Thus,

    The side of cube with surface area 480 sq. meters is  0.91 meters longer than the side of cube with 270 sq. meters surface area.

    Learn more about surface area of cube here;

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