Which of the following is true about the diameter of a sphere?(1 point)
Responses
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 the shortest length on a sphere.
The diameter is the shortest length on a sphere.
The diameter is not a chord.
The diameter is not a chord.
The diameter is 2.5 times the length of the radius.
4.5 in. × 4.5 in. × 4.5 in. is corect
The first two statements are correct:
1. The diameter of a sphere passes through the center of the circle.
2. The diameter is the shortest length on a sphere.
The third statement is incorrect:
3. The diameter is not a chord.
The fourth statement is also incorrect:
4. The diameter is not 2.5 times the length of the radius.
just one
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
66.44 in.2
66.44 inches squared
84.64 in.2
To find the surface area of a sphere, we use the formula:
Surface Area = 4πr^2
Given that the diameter of the basketball is 9.2 inches, the radius can be calculated by dividing the diameter by 2:
Radius = 9.2 inches / 2 = 4.6 inches
Substituting this radius value into the formula:
Surface Area = 4 * 3.14 * (4.6)^2
Surface Area ≈ 265.77 in.²
Therefore, the correct answer is:
265.77 in.²
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, we use the formula:
Surface Area = 4πr^2
Given that the diameter of the sphere is 30 inches, the radius can be calculated by dividing the diameter by 2:
Radius = 30 inches / 2 = 15 inches
Substituting this radius value into the formula:
Surface Area = 4 * π * (15)^2
Surface Area = 4 * π * 225
Surface Area = 900π in.²
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
4.5 in. × 4.5 in. × 4.5 in.
4.5 inches times 4.5 inches times 4.5 inches
1.2 in. × 1.2 in. × 1.2 in.
1.2 inches times 1.2 inches times 1.2 inches
2.25 in. × 2.25 in. × 2.25 in.
2.25 inches times 2.25 inches times 2.25 inches
4 in.× 4 in.× 4 in.
To find the dimensions of the cube box that can snugly fit the spherical soaps, we need to calculate the edge length of the cube using the surface area of the soap.
The surface area of a cube can be calculated using the formula:
Surface Area = 6s^2
where s is the length of each side of the cube.
Given that the surface area of the soap is 63.585 in.², we can set up the equation:
63.585 = 6s^2
To solve for s, we can divide both sides by 6 and then take the square root:
s^2 = 63.585 / 6
s^2 ≈ 10.5975
s ≈ √10.5975
s ≈ 3.25 inches
Therefore, the dimensions of the cube box should be approximately:
3.25 in. × 3.25 in. × 3.25 in.
However, none of the given options match this result, so none of the provided responses are correct.