Find the surface area of a sphere that has a radius of 57 inches. Use 3.14 for π.
The sphere's surface area is _______ square inches.
The formula to calculate the surface area of a sphere is 4πr^2, where r is the radius.
Plugging in the given radius of 57 inches into the formula:
Surface area = 4π(57)^2
Surface area = 4π(3249)
Surface area = 12996π
Using π ≈ 3.14,
Surface area ≈ 12996 * 3.14
Surface area ≈ 40847.44 square inches
Therefore, the surface area of the sphere with a radius of 57 inches is approximately 40847.44 square inches.
wrong
I apologize for the mistake. Let's recalculate it using the correct formula.
The formula for the surface area of a sphere is given by:
Surface Area = 4πr^2
Given that the radius of the sphere is 57 inches, we can plug this into the formula:
Surface Area = 4 * 3.14 * (57)^2
Surface Area = 4 * 3.14 * 3249
Surface Area = 40765.04 square inches
Therefore, the surface area of the sphere with a radius of 57 inches is 40765.04 square inches.
A ball will fit inside a cubed box and will touch all six sides. The surface area of the ball is 803.84 square inches. What is the length of each side of the box? Use 3.14 for π.
When a ball is placed inside a cube such that it touches all six sides of the cube, the ball's diameter is equal to the side length of the cube.
Given that the surface area of the ball is 803.84 square inches, we can calculate the radius of the ball using its surface area:
Surface Area of sphere = 4πr^2
803.84 = 4 * 3.14 * r^2
803.84 = 12.56 * r^2
r^2 = 803.84 / 12.56
r^2 = 64
r = 8 inches
Since the diameter of the ball is equal to the side length of the cube:
Side length of the cube = 2r = 2 * 8 = 16 inches
Therefore, the length of each side of the cube is 16 inches.