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 an edge.
9 answers
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 is 2.5 times the length of the radius.
The diameter is 2.5 times the length of the radius.
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.
Responses
The diameter is not a chord.
The diameter is not a chord.
The diameter is 2.5 times the length of the radius.
The diameter is 2.5 times the length of the radius.
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 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
1,063.08 in.2
1,063.08 inches squared
66.44 in.2
66.44 inches squared
84.64 in.2
84.64 inches squared
265.77 in.2
Responses
1,063.08 in.2
1,063.08 inches squared
66.44 in.2
66.44 inches squared
84.64 in.2
84.64 inches squared
265.77 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 (r) is half of the diameter, so r = 9.2/2 = 4.6 inches.
Substituting this value into the formula, we get:
Surface Area = 4 * 3.14 * (4.6)^2
= 4 * 3.14 * 21.16
= 265.77 in.2
Therefore, the surface area of the basketball is 265.77 in.2.
Surface Area = 4πr^2
Given that the diameter of the basketball is 9.2 inches, the radius (r) is half of the diameter, so r = 9.2/2 = 4.6 inches.
Substituting this value into the formula, we get:
Surface Area = 4 * 3.14 * (4.6)^2
= 4 * 3.14 * 21.16
= 265.77 in.2
Therefore, the surface area of the basketball 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
3,600π in.2
3,600 pi inches squared
900π in.2
900 pi inches squared
225π in.2
225 pi inches squared
2,826π in.2
2,826 pi inches squared
Responses
3,600π in.2
3,600 pi inches squared
900π in.2
900 pi inches squared
225π in.2
225 pi inches squared
2,826π in.2
2,826 pi inches squared
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 (r) is half of the diameter, so r = 30/2 = 15 inches.
Substituting this value into the formula, we get:
Surface Area = 4 * π * (15)^2
= 4 * π * 225
= 900π in.2
Therefore, the surface area of the sphere is 900π in.2.
Surface Area = 4πr^2
Given that the diameter of the sphere is 30 inches, the radius (r) is half of the diameter, so r = 30/2 = 15 inches.
Substituting this value into the formula, we get:
Surface Area = 4 * π * (15)^2
= 4 * π * 225
= 900π in.2
Therefore, the surface area of the sphere 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
2.25 in. × 2.25 in. × 2.25 in.
2.25 inches times 2.25 inches times 2.25 inches
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.
Responses
4.5 in. × 4.5 in. × 4.5 in.
4.5 inches times 4.5 inches times 4.5 inches
2.25 in. × 2.25 in. × 2.25 in.
2.25 inches times 2.25 inches times 2.25 inches
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.
To find the dimensions of the cube box, we need to find the edge length of the cube. Since all edges of a cube are equal, we can find the edge length by taking the cube root of the volume of the cube.
The surface area of the spherical soap is given as 63.585 in.2.
To find the volume of the cube, we divide the surface area of the soap by 6 (as there are 6 faces in a cube):
Volume of the cube = Surface Area of the soap / 6
Volume of the cube = 63.585 / 6
Volume of the cube ≈ 10.5975 in.^3
Taking the cube root of the volume, we find the edge length of the cube:
Edge Length = ∛10.5975
Edge Length ≈ 2.15 in.
Therefore, the dimensions of the cube box should be approximately 2.15 inches by 2.15 inches by 2.15 inches.
The surface area of the spherical soap is given as 63.585 in.2.
To find the volume of the cube, we divide the surface area of the soap by 6 (as there are 6 faces in a cube):
Volume of the cube = Surface Area of the soap / 6
Volume of the cube = 63.585 / 6
Volume of the cube ≈ 10.5975 in.^3
Taking the cube root of the volume, we find the edge length of the cube:
Edge Length = ∛10.5975
Edge Length ≈ 2.15 in.
Therefore, the dimensions of the cube box should be approximately 2.15 inches by 2.15 inches by 2.15 inches.
9 answers