A cube box is 20 cm×20 cm× 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.(1 point)
The diameter of the largest size sphere that can fit in the box is equal to the length of one side of the cube, which is 20 cm.
The radius of the sphere is half of the diameter, so it is 20 cm / 2 = 10 cm.
The surface area of a sphere is given by the formula 4πr^2, where r is the radius.
Plugging in the radius, we get 4π(10 cm)^2 = 400π cm^2.
Therefore, the surface area of the largest size sphere that can fit in the cube box is 400π cm^2.
Find the surface area of a sphere with a diameter of 40 inches. Leave your answer in terms of pi.(1 point) The surface area is in.2
The radius of the sphere is half of the diameter, so it is 40 inches / 2 = 20 inches.
The surface area of a sphere is given by the formula 4πr^2, where r is the radius.
Plugging in the radius, we get 4π(20 inches)^2 = 1600π square inches.
Therefore, the surface area of the sphere with a diameter of 40 inches is 1600π square inches.
Find the surface area of a sphere with a radius of 3.6 ft. Use 3.14 for pi. Round your answer to the nearest hundredth, if necessary.(1 point) The surface area is ft.2
The surface area of a sphere is given by the formula 4πr^2, where r is the radius.
Plugging in the radius, we get 4 * 3.14 * (3.6 ft)^2 = 162.14 ft^2.
Therefore, the surface area of the sphere with a radius of 3.6 ft is approximately 162.14 ft^2.
A rectangular box is 12 in. × 14 in. × 18 in. What is the surface area of the largest size sphere that could fit in this box? Leave your answer in terms of pi.(1 point) in2
To find the largest size sphere that can fit in a rectangular box, we need to find the diameter of the sphere, which will be equal to the smallest side length of the box.
Out of the dimensions provided, the box has a dimension of 12 in x 14 in x 18 in.
The smallest side length is 12 in, so the diameter of the largest size sphere that can fit in this box is 12 in.
The surface area of a sphere is given by the formula 4πr^2, where r is the radius.
Since the radius is half of the diameter, the radius is 12 in / 2 = 6 in.
Plugging in the radius, we get 4π(6 in)^2 = 144π in^2.
Therefore, the surface area of the largest size sphere that can fit in the rectangular box is 144π in^2.