A cute boxes 20 cm x 20cm x 20cm what is the surface area of the largest size sphere that can fit in the box leave your answer in term of pi
The diameter of the sphere is equal to the diagonal of the box, since it will touch two opposite corners of the cube.
Using the Pythagorean theorem, the diagonal of the box can be calculated as follows:
Diagonal^2 = (Length^2) + (Width^2) + (Height^2)
Diagonal^2 = (20cm)^2 + (20cm)^2 + (20cm)^2
Diagonal^2 = 400cm^2 + 400cm^2 + 400cm^2
Diagonal^2 = 1200cm^2 + 400cm^2
Diagonal^2 = 1600cm^2
Taking the square root of both sides, we get:
Diagonal = √1600cm^2
Diagonal = 40cm
The radius of the sphere is half the diameter, so the radius of the sphere is:
Radius = 40cm / 2
Radius = 20cm
The surface area of the sphere is given by the formula:
Surface area = 4πr^2
Plugging in the value of the radius, we get:
Surface area = 4π(20cm)^2
Surface area = 4π(400cm^2)
Surface area = 1600π cm^2
Therefore, the surface area of the largest sphere that can fit in the given box is 1600π cm^2.