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3 April, 11:32

A rectangular solid whose edges are 4 cm, 5 cm, and 7cm is inscribed in a sphere., Find the volume and the surface area of the sphere.

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  1. 3 April, 11:50
    0
    Equation of a sphere with radius r is given by x^2 + y^2 + z^2 = r^2

    For a rectangular solid inscribes on a sphere, the sides are 2x by 2y by 2z, putting this into the equation of a sphere, we have

    (4/2) ^2 + (5/2) ^2 + (7/2) ^2 = r^2

    r^2 = 4 + 25/4 + 49/4 = 45/2

    r = sqrt (45/2) = 4.74

    Now, volume of sphere is given by 4/3πr^3 = 4/3π (4.74) ^3 = 142.3π = 447.1 cm^3

    Also, surface area of a sphere is given by = 4πr^2 = 4π (4.74) ^2 = 90π = 282.7 cm^2
  2. 3 April, 11:52
    0
    The answer is:

    Surface Area=433cm^2

    Volume=144.5cm^3
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