Which of the following correctly describes a sphere?(1 point)
Responses
A sphere has a center.
A sphere has a center.
A sphere has a face.
A sphere has a face.
A sphere has a vertex.
A sphere has a vertex.
A sphere has an edge.
A sphere has a center.
Which of the following is true about the diameter of a sphere?(1 point)
Responses
The diameter is not a chord.
The diameter is not a chord.
The diameter of a sphere passes through the center of the circle.
The diameter of a sphere passes through the center of the circle.
The diameter is 2.5 times the length of the radius.
The diameter is 2.5 times the length of the radius.
The diameter is the shortest length on a sphere.
The diameter of a sphere passes through the center of the circle.
Use the formula for the surface area of a sphere to find the surface area of a basketball that has a diameter of 9.2 inches. Use 3.14 pi and round your answer to the nearest hundredth, if necessary.(1 point)
Responses
265.77 in.2
265.77 inches squared
1,063.08 in.2
1,063.08 inches squared
84.64 in.2
84.64 inches squared
66.44 in.2
To find the surface area of a sphere, you can use the formula:
Surface Area = 4 * π * r^2
Since the diameter is given, you can find the radius by dividing the diameter by 2:
Radius = 9.2 / 2 = 4.6 inches
Substituting this value into the formula:
Surface Area = 4 * 3.14 * (4.6)^2
Surface Area ≈ 265.77 inches squared
Therefore, the correct answer is:
265.77 inches squared
Find the surface area of a sphere with a diameter of 30 inches. Leave your answer in terms of pi.(1 point)
Responses
225π in.2
225 pi inches squared
3,600π in.2
3,600 pi inches squared
2,826π in.2
2,826 pi inches squared
900π in.2
To find the surface area of a sphere, you can use the formula:
Surface Area = 4 * π * r^2
Given that the diameter is 30 inches, you can find the radius by dividing the diameter by 2:
Radius = 30 / 2 = 15 inches
Substituting this value into the formula:
Surface Area = 4 * π * (15)^2
Surface Area = 4 * π * 225
Surface Area = 900π
Therefore, the correct answer is:
900π in.2
Marcus is making spherical soaps to sell in his online store. The surface area of a soap is 63.585 in.2 and he wants to package them into a cube box so that it fits snugly. Using 3.14 as the value of pi, what should be the dimensions of the cube box?(1 point)
Responses
1.2 in. × 1.2 in. × 1.2 in.
1.2 inches times 1.2 inches times 1.2 inches
4 in.× 4 in.× 4 in.
4 inches times 4 inches times 4 inches
2.25 in. × 2.25 in. × 2.25 in.
2.25 inches times 2.25 inches times 2.25 inches
4.5 in. × 4.5 in. × 4.5 in.
To determine the dimensions of the cube box that will snugly fit the soap, we need to find the edge length of the cube.
Given that the surface area of the soap is 63.585 square inches, we can find the length of each side of the cube by taking the square root of the surface area:
Edge Length = √(Surface Area/6)
Edge Length = √(63.585/6)
Edge Length ≈ √(10.5975)
Edge Length ≈ 3.25 inches (rounded to the nearest hundredth)
Therefore, the correct answer is:
3.25 inches × 3.25 inches × 3.25 inches