The longest possible diagonal of the cube will pass through its opposite corners. By using the Pythagorean theorem, we can calculate this diagonal as follows:
d = √(20^2 + 20^2 + 20^2)
= √(400 + 400 + 400)
= √1200
= 20√3
The diagonal represents the diameter of the largest sphere that can fit inside the cube. Therefore, the radius of the sphere is half the diameter, which is:
r = (20√3)/2
= 10√3
The surface area of the sphere is given by the formula:
A = 4πr^2
Substituting the value of r, we get:
A = 4π(10√3)^2
= 4π(100 × 3)
= 4π(300)
= 1200π
Therefore, the surface area of the largest size sphere that can fit inside the cube is 1200π square cm.
A cube box is 20cm * 20cm * 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.
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1 answer