To determine the surface area of the largest size sphere that can fit in the box, we need to find the diameter of the sphere first. Since the box is a cube with side length 20 cm, the diagonal of the cube will pass through the center of the sphere and will be equal to the diameter of the sphere.
Using the Pythagorean theorem, we can find the diagonal of the cube:
diagonal^2 = side^2 + side^2 + side^2
= 3 * (side^2)
= 3 * (20 cm)^2 = 1200 cm^2
diagonal = sqrt(1200 cm^2) = 34.64 cm
The diameter of the sphere will be equal to the diagonal, which is 34.64 cm.
The surface area of a sphere is given by the formula:
surface area = 4 * pi * radius^2
Since the radius is half the diameter, the radius of the sphere is r = 34.64 cm / 2 = 17.32 cm.
Therefore, the surface area of the largest size sphere that can fit in the box is:
surface area = 4 * pi * (17.32 cm)^2 = 4 * pi * 299.2384 cm^2
Hence, the surface area of the largest size sphere that can fit in the box is approximately 1196.9536 cm^2 * pi.
A cute box is 20 cm * 20 cm * 20 cm what is the surface area of the largest size fear that can fit in the box leave your answer in terms of pi
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