A cube box is 20 cm×20 cm× 20 cm
. What is the surface area of the largest size sphere that can fit in this box? Leave your answer in terms of pi.(1 point)
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The largest size sphere that can fit inside the cube box would have a diameter equal to the side length of the cube, which is 20 cm.
The surface area of a sphere is given by the formula:
$$A = 4\pi r^2$$
where r is the radius of the sphere.
Since the diameter (d) of the sphere is equal to 20 cm, the radius (r) would be half of the diameter:
$$r = \frac{d}{2} = \frac{20 cm}{2} = 10 cm$$
Now we can substitute this radius value into the surface area formula:
$$A = 4\pi (10)^2 = 4\pi(100) = 400\pi \, cm^2$$
Therefore, the surface area of the largest size sphere that can fit in the cube box is 400π cm^2. Answer: \boxed{400\pi}.