Question

Use the formula for the volume of a sphere to find the volume of a basketball that has a diameter of 9.2 inches. Use 3.14 as an approximation for pi and round your answer to the nearest hundredth, if necessary.(1 point)

Responses

3,260.11 in.3
3,260.11 inches cubed
115.55 in.3
115.55 inches cubed
1,222.54 in.3
1,222.54 in cubed
407.51 in.3
407.51 inches cubed

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the volume of a sphere, you can use the formula:

V = (4/3) * π * r^3

Given that the diameter of the basketball is 9.2 inches, you can find the radius by dividing the diameter by 2:

r = 9.2 / 2 = 4.6 inches

Now, substitute the value of the radius into the formula:

V = (4/3) * 3.14 * (4.6)^3

V ≈ 407.51 in^3

Answer 2

Find the volume of a sphere with a radius of 1.8 yards. Leave your answer in terms of pi. Round your answer to the nearest hundredth, if necessary.(1 point)

Responses

24.43π yds3
24.43 pi yds cubed
7.2π yds3
7.2 pi yds cubed
23.34π yds3
23.34 pi yds cubed
7.78π yds3

Answer 3

[AI-generated answer — Bot GPT 3.5]

To find the volume of a sphere, you can use the formula:

V = (4/3) * π * r^3

Given that the radius of the sphere is 1.8 yards, plug this value into the formula:

V = (4/3) * π * (1.8)^3

V ≈ 24.43π yds^3

Answer 4

Use the formula for the volume of a sphere to solve the following problem.

How much air is needed to fill a basketball with a diameter of 9 inches? Use 3.14 as an approximation for pi. Round your answer to the nearest tenth.
(1 point)
Responses

113 in.3
113 inches cubed
190.8 in.3
190.8 inches cubed
3,052.1 in.3
3,052.1 inches cubed
381.5 in.3

Answer 5

[AI-generated answer — Bot GPT 3.5]

To find the volume of the basketball, you can use the formula for the volume of a sphere:

V = (4/3) * π * r^3

First, find the radius by dividing the diameter by 2:

r = 9 / 2 = 4.5 inches

Now, substitute the radius into the formula:

V = (4/3) * 3.14 * (4.5)^3

V ≈ 381.5 in^3

Therefore, approximately 381.5 cubic inches of air is needed to fill the basketball.

Answer 6

The volume of a container measures 4,000 mm3 and contains 50 marbles. Each marble has a radius of 2 mm. Use 3.14 as an approximation for pi. How much space in the box is unused? Round your answer to the nearest tenth.(1 point)

Responses

3,900 mm3
3,900 mm cubed
1,674.7 mm3
1,674.7 mm cubed
2,325.3 mm3
2,325.3 mm cubed
33.5 mm3

Answer 7

[AI-generated answer — Bot GPT 3.5]

To find the space unused in the box, we need to calculate the total volume of the marbles and subtract it from the volume of the container.

The volume of one marble can be calculated using the formula for the volume of a sphere:

V = (4/3) * π * r^3

Given that the radius of each marble is 2 mm, we can substitute this value into the formula:

V = (4/3) * 3.14 * (2)^3

V ≈ 33.49 mm^3 (rounded to the nearest hundredth)

To find the total volume of all the marbles, we multiply the volume of one marble by the number of marbles:

Total volume of marbles = 33.49 mm^3 * 50 = 1674.5 mm^3

Now, subtract the total volume of the marbles from the volume of the container to find the unused space:

Unused space = 4000 mm^3 - 1674.5 mm^3 ≈ 2325.5 mm^3

So, approximately 2325.5 cubic millimeters of space is unused in the box.

Answer 8

THATS NOT ANSWER

Answer 9

[AI-generated answer — Bot GPT 3.5]

Apologies for the mistake.

To find the volume of the marbles, we need to calculate the volume of each marble and then multiply it by the number of marbles.

The volume of a marble can be calculated using the formula for the volume of a sphere:

V = (4/3) * π * r^3

Given that the radius of each marble is 2 mm, we can substitute this value into the formula:

V = (4/3) * 3.14 * (2)^3

V ≈ 33.49 mm^3 (rounded to the nearest hundredth)

To find the total volume of all the marbles, we multiply the volume of one marble by the number of marbles:

Total volume of marbles = 33.49 mm^3 * 50 = 1674.5 mm^3

To find the unused space in the box, subtract the volume of the marbles from the volume of the container:

Unused space = 4000 mm^3 - 1674.5 mm^3 ≈ 2325.5 mm^3

Therefore, approximately 2325.5 cubic millimeters of space is unused in the box.

Answer 10

Kairay created a sculpture by forming a hemisphere with a radius of 20 inches and then removing a hemisphere with a radius of 15 inches from it. Calculate the volume of his sculpture. Use 3.14 as an approximation for pi. Round your answer to the nearest whole number.(1 point)

Responses

19,363 in.3
19,363 inches cubed
16,747 in.3
16,747 inches cubed
7,065 in.3
7,065 inches cubed
9,682 in.3

Answer 11

[AI-generated answer — Bot GPT 3.5]

To calculate the volume of Kairay's sculpture, we first need to find the volume of the larger hemisphere and then subtract the volume of the smaller hemisphere that was removed.

The volume of a hemisphere can be calculated using the formula:

V = (2/3) * π * r^3

For the larger hemisphere with a radius of 20 inches:

V1 = (2/3) * 3.14 * (20)^3

V1 ≈ 33,493 in^3 (rounded to the nearest whole number)

For the smaller hemisphere with a radius of 15 inches:

V2 = (2/3) * 3.14 * (15)^3

V2 ≈ 14,137 in^3 (rounded to the nearest whole number)

To find the volume of Kairay's sculpture, subtract V2 from V1:

Volume of sculpture = V1 - V2 = 33,493 in^3 - 14,137 in^3 = 19,356 in^3

Therefore, the volume of Kairay's sculpture is approximately 19,356 inches cubed.