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 the shortest length on a sphere.
The diameter is the shortest length on a sphere.
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 correct response is:
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
84.64 in.2
84.64 inches squared
66.44 in.2
66.44 inches squared
265.77 in.2
265.77 inches squared
1,063.08 in.2
To find the surface area of a sphere, we use the formula:
Surface Area = 4πr^2
Given the diameter of 9.2 inches, we can find the radius by dividing the diameter by 2:
Radius = 9.2 / 2 = 4.6 inches
Now, we can plug the radius into the formula:
Surface Area = 4 * 3.14 * (4.6)^2
Surface Area ≈ 4 * 3.14 * 21.16
Surface Area ≈ 265.76 in^2
Rounded to the nearest hundredth, the surface area is approximately 265.77 in^2.
The correct response 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
900π in.2
900 pi inches squared
3,600π in.2
3,600 pi inches squared
2,826π in.2
2,826 pi inches squared
225π in.2
225 pi inches squared
To find the surface area of a sphere, we use the formula:
Surface Area = 4πr^2
Given the diameter of 30 inches, we can find the radius by dividing the diameter by 2:
Radius = 30 / 2 = 15 inches
Now, we can plug the radius into the formula:
Surface Area = 4 * π * (15)^2
Surface Area = 4 * π * 225
Surface Area = 900 * π
Therefore, the surface area of the sphere with a diameter of 30 inches is 900π in^2.
The correct response 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
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.
4 inches times 4 inches times 4 inches
4.5 in. × 4.5 in. × 4.5 in.
To find the dimensions of the cube box that will snugly fit the spherical soaps, we need to find the side length of the cube.
The surface area of the soap is given as 63.585 square inches.
The formula for the surface area of a cube is:
Surface Area = 6s^2
where s is the side length of the cube.
We can set up the equation:
63.585 = 6s^2
Dividing both sides by 6:
10.5975 = s^2
Taking the square root of both sides:
s ≈ √10.5975
s ≈ 3.26 inches
Therefore, the approximate side length of the cube box should be 3.26 inches.
The correct response is:
4 in. × 4 in. × 4 in.
Use the paragraph to answer the question.
(1) Our town's plastic bag ban is a wise policy. (2) Studies have demonstrated the detrimental effects plastic bags have on the environment. (3) People have argued that banning plastic bags will only result in the increased use of paper bags, simply causing a different environmental problem. (4) However, paper bags can be recycled more effectively than plastic bags. (5) We should all support the new policy on plastic bags.
In which sentence does the author refute an opposing argument?
(1 point)
Responses
sentence 5
sentence 5
sentence 3
sentence 3
sentence 2
sentence 2
sentence 4
sentence 4
The sentence in which the author refutes an opposing argument is:
sentence 4.
Which would be a sound argument for the proposition that a community should sponsor a riverfront clean-up day?(1 point)
Responses
Students need more community service hours for graduation, and a clean-up day is a fun option.
Students need more community service hours for graduation, and a clean-up day is a fun option.
Many people in our community enjoy walking by the riverfront.
Many people in our community enjoy walking by the riverfront.
A clean-up day would bring the community together on a project to reduce pollution and beautify the parks.
A clean-up day would bring the community together on a project to reduce pollution and beautify the parks.
The Ohio River is nearly 1,000 miles long from end to end, and that's more than one-third of the length of the Mississippi River.
The sound argument for the proposition that a community should sponsor a riverfront clean-up day is:
A clean-up day would bring the community together on a project to reduce pollution and beautify the parks.