First, we need to find the radius of the basketball by dividing the diameter by 2:
Radius = 9.2 inches / 2 = 4.6 inches
Now, we can use the formula for the volume of a sphere:
V = (4/3) * π * r^3
V = (4/3) * 3.14 * (4.6)^3
V = (4/3) * 3.14 * 97.336
V ≈ 407.51 inches cubed
Therefore, the volume of the basketball is 407.51 inches cubed.
Answer: 407.51 inches cubed
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 407.51 in.3 407.51 inches cubed 3,260.11 in.3 3,260.11 inches cubed 1,222.54 in.3 1,222.54 in cubed 115.55 in.3
9 answers
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
We can use the formula for the volume of a sphere:
V = (4/3) * π * r^3
Given that the radius is 1.8 yards, we substitute this into the formula:
V = (4/3) * π * (1.8)^3
V = (4/3) * π * 5.832
V = 7.776π
Rounded to the nearest hundredth, the volume of the sphere with a radius of 1.8 yards is:
7.78π yds³
Answer: 7.78π yds³
V = (4/3) * π * r^3
Given that the radius is 1.8 yards, we substitute this into the formula:
V = (4/3) * π * (1.8)^3
V = (4/3) * π * 5.832
V = 7.776π
Rounded to the nearest hundredth, the volume of the sphere with a radius of 1.8 yards is:
7.78π yds³
Answer: 7.78π yds³
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 381.5 in.3 381.5 inches cubed 3,052.1 in.3 3,052.1 inches cubed 113 in.3 113 inches cubed 190.8 in.3
First, we need to find the radius of the basketball by dividing the diameter by 2:
Radius = 9 inches / 2 = 4.5 inches
Now, we can use the formula for the volume of a sphere:
V = (4/3) * π * r^3
V = (4/3) * 3.14 * (4.5)^3
V = (4/3) * 3.14 * 91.125
V ≈ 381.53 inches cubed
Therefore, the amount of air needed to fill the basketball is approximately 381.5 inches cubed.
Answer: 381.5 inches cubed
Radius = 9 inches / 2 = 4.5 inches
Now, we can use the formula for the volume of a sphere:
V = (4/3) * π * r^3
V = (4/3) * 3.14 * (4.5)^3
V = (4/3) * 3.14 * 91.125
V ≈ 381.53 inches cubed
Therefore, the amount of air needed to fill the basketball is approximately 381.5 inches cubed.
Answer: 381.5 inches cubed
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 33.5 mm3 33.5 mm cubed 1,674.7 mm3 1,674.7 mm cubed 2,325.3 mm3 2,325.3 mm cubed 3,900 mm3
First, we find the volume of one marble using the formula V = (4/3) * π * r^3, where r = 2 mm:
V = (4/3) * 3.14 * (2)^3
V = (4/3) * 3.14 * 8
V = 33.51 mm³ (approx. 33.5 mm³)
Next, we calculate the total volume taken up by 50 marbles:
Total Volume of marbles = 33.5 mm³ * 50 = 1675 mm³
Now, we find the remaining space in the box by subtracting the total volume of the marbles from the total volume of the box:
Remaining Space = 4000 mm³ - 1675 mm³ = 2325 mm³
Therefore, the amount of space in the box that is unused is 2325 mm³.
Answer: 2,325.3 mm³
V = (4/3) * 3.14 * (2)^3
V = (4/3) * 3.14 * 8
V = 33.51 mm³ (approx. 33.5 mm³)
Next, we calculate the total volume taken up by 50 marbles:
Total Volume of marbles = 33.5 mm³ * 50 = 1675 mm³
Now, we find the remaining space in the box by subtracting the total volume of the marbles from the total volume of the box:
Remaining Space = 4000 mm³ - 1675 mm³ = 2325 mm³
Therefore, the amount of space in the box that is unused is 2325 mm³.
Answer: 2,325.3 mm³
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 7,065 in.3 7,065 inches cubed 16,747 in.3 16,747 inches cubed 19,363 in.3 19,363 inches cubed 9,682 in.3
The volume of the sculpture can be calculated by first finding the volume of the larger hemisphere with radius 20 inches and then subtracting the volume of the smaller hemisphere with radius 15 inches.
Volume of larger hemisphere:
V1 = (2/3) * π * r1^3
V1 = (2/3) * 3.14 * 20^3
V1 = (2/3) * 3.14 * 8000
V1 = 16,747 inches cubed (rounded to the nearest whole number)
Volume of smaller hemisphere:
V2 = (2/3) * π * r2^3
V2 = (2/3) * 3.14 * 15^3
V2 = (2/3) * 3.14 * 3375
V2 = 7065 inches cubed
Volume of sculpture = V1 - V2
Volume of sculpture = 16,747 - 7065
Volume of sculpture = 9,682 inches cubed
Therefore, the volume of Kairay's sculpture is 9,682 inches cubed.
Answer: 9,682 inches cubed
Volume of larger hemisphere:
V1 = (2/3) * π * r1^3
V1 = (2/3) * 3.14 * 20^3
V1 = (2/3) * 3.14 * 8000
V1 = 16,747 inches cubed (rounded to the nearest whole number)
Volume of smaller hemisphere:
V2 = (2/3) * π * r2^3
V2 = (2/3) * 3.14 * 15^3
V2 = (2/3) * 3.14 * 3375
V2 = 7065 inches cubed
Volume of sculpture = V1 - V2
Volume of sculpture = 16,747 - 7065
Volume of sculpture = 9,682 inches cubed
Therefore, the volume of Kairay's sculpture is 9,682 inches cubed.
Answer: 9,682 inches cubed
1 answer