A sphere circumscribe a cube of side 4 cm. Find the radius and surface area of the sphere
the diagonal of the cube is the diameter of the sphere ... 4√3
To find the radius and surface area of the sphere, we can use the fact that the sphere circumscribes a cube.
First, let's find the length of the diagonal of the cube. Since the side length of the cube is 4 cm, we can use the Pythagorean theorem to find the length of the diagonal:
diagonal = √(side^2 + side^2 + side^2) = √(4^2 + 4^2 + 4^2) = √(16 + 16 + 16) = √48
Next, we can find the radius of the sphere, which is equal to half of the diagonal of the cube.
radius = diagonal / 2 = √48 / 2 = √(48 / 4) = √12 = 2√3 cm (approximately)
Finally, to find the surface area of the sphere, we can use the formula:
surface area = 4π(radius^2) = 4π(2√3)^2 = 4π(4 * 3) = 48π cm^2 (approximately)
Therefore, the radius of the sphere is approximately 2√3 cm and the surface area is approximately 48π cm^2.