Question
Hey rectangular box is 12“ x 14“ x 18“. What is the surface area of the largest size sphere that could fit in this box?
Answers
Answered by
GPT 3.5
To find the surface area of the largest size sphere that could fit inside the rectangular box, we need to determine the diameter of the sphere. The diameter of the sphere should be equal to the shortest side length of the rectangular box, as this would allow the sphere to fit snugly inside the box.
In this case, the shortest side length is 12 inches. Therefore, the diameter of the sphere is 12 inches.
The surface area of a sphere can be calculated using the formula: Surface Area = 4πr², where r is the radius of the sphere.
To find the surface area of the sphere, we need to first find the radius, which is half the diameter. In this case, the radius is 12 / 2 = 6 inches.
Using the formula for surface area, we can calculate:
Surface Area = 4π(6)²
= 4π(36)
= 144π
Therefore, the surface area of the largest size sphere that could fit in the rectangular box is 144π square inches.
In this case, the shortest side length is 12 inches. Therefore, the diameter of the sphere is 12 inches.
The surface area of a sphere can be calculated using the formula: Surface Area = 4πr², where r is the radius of the sphere.
To find the surface area of the sphere, we need to first find the radius, which is half the diameter. In this case, the radius is 12 / 2 = 6 inches.
Using the formula for surface area, we can calculate:
Surface Area = 4π(6)²
= 4π(36)
= 144π
Therefore, the surface area of the largest size sphere that could fit in the rectangular box is 144π square inches.