A cube box is 20 cm * 20cm * 20cm What is the surface area of the largest size sphere that can fit in this box? Leave your answer in ter of pl. it point
To find the largest size sphere that can fit inside a cube, we need to find the length of the diagonal of the cube.
Using the Pythagorean theorem, we can calculate the length of the diagonal:
diagonal = sqrt(side^2 + side^2 + side^2)
diagonal = sqrt(20^2 + 20^2 + 20^2)
diagonal = sqrt(1200)
diagonal ≈ 34.64 cm
The diameter of the largest sphere that can fit inside the cube is equal to the length of the diagonal. Therefore, the diameter of the sphere is 34.64 cm.
The surface area of a sphere is given by the formula:
surface area = 4πr^2
Since the diameter is given, we can find the radius of the sphere:
radius = diameter / 2
radius = 34.64 / 2
radius ≈ 17.32 cm
Now we can calculate the surface area of the sphere:
surface area = 4π(17.32)^2
surface area ≈ 4π(299.95)
surface area ≈ 1199.79π cm^2
Therefore, the surface area of the largest size sphere that can fit in the cube box is approximately 1199.79π cm^2.
NONSENSE bot! Yours fits OUTSIDE the cube
really R = 1/2 length of cube side.
R = 10 cm
4 pi r^2 = 4 pi * 100 = 400 pi cm^2
Apologies for the previous incorrect response. You are correct.
To find the largest sphere that can fit inside a cube, we can use the radius as half the length of a side of the cube. In this case, the radius would be 10 cm.
Using the formula for the surface area of a sphere, which is 4πr^2, we can calculate the surface area:
surface area = 4π(10)^2
surface area = 4π(100)
surface area = 400π cm^2
Therefore, the surface area of the largest size sphere that can fit in the cube box is 400π cm^2.
To find the surface area of the largest sphere that can fit inside the cube box, we need to determine the diameter of the sphere first. Once we have the diameter, we can use the formula for the surface area of a sphere to find the answer.
The diagonal of the cube can be calculated using the Pythagorean theorem:
Diagonal = √(length² + width² + height²)
= √(20² + 20² + 20²)
= √(400 + 400 + 400)
= √1200
= 20√3 cm
Since the diameter of the sphere is equal to the diagonal of the cube, the diameter is 20√3 cm.
The formula for the surface area of a sphere is:
Surface Area = 4πr²
To find the radius of the sphere, we divide the diameter by 2:
Radius = Diameter / 2
= 20√3 cm / 2
= 10√3 cm
Now, we can substitute the radius into the surface area formula:
Surface Area = 4π(10√3)²
= 4π(100 × 3)
= 1200π cm²
Therefore, the surface area of the largest sphere that can fit inside the cube box is 1200π cm².