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
407.51 in.3
407.51 inches cubed
1,222.54 in.3
1,222.54 in cubed
115.55 in.3
To find the volume of a basketball, we can use the formula V = (4/3) * π * r^3, where V is the volume, π is pi, and r is the radius.
Since the basketball has a diameter of 9.2 inches, the radius is half of that, which is 4.6 inches.
Now we can substitute the values into the formula:
V = (4/3) * 3.14 * (4.6)^3
V ≈ 407.51 in.3
Therefore, the volume of the basketball is approximately 407.51 inches cubed.
To find the volume of a sphere, we can use the formula V = (4/3) * π * r^3, where V is the volume, π is pi, and r is the radius.
Given that the radius is 1.8 yards, we can substitute this value into the formula:
V = (4/3) * π * (1.8)^3
V ≈ 24.43π yds^3
Therefore, the volume of the sphere with a radius of 1.8 yards is approximately 24.43π yds cubed.
To find the volume of a sphere, we can use the formula V = (4/3) * π * r^3, where V is the volume, π is pi, and r is the radius.
Given that the diameter of the basketball is 9 inches, we need to find the radius by dividing the diameter by 2:
radius = 9 inches / 2 = 4.5 inches
Substituting this radius value into the formula, we have:
V = (4/3) * 3.14 * (4.5)^3
V ≈ 381.5 in^3
Therefore, approximately 381.5 inches cubed of air is needed to fill the basketball.
To find the unused space in the box, we need to subtract the total volume of the marbles from the volume of the container.
First, let's find the volume of each marble using the formula for a sphere: V = (4/3) * π * r^3.
Given that the radius of each marble is 2 mm, we can calculate the volume:
V = (4/3) * 3.14 * (2)^3
V ≈ 33.49 mm^3 (rounded to the nearest hundredth)
Since there are 50 marbles, the total volume of the marbles is:
50 * 33.49 mm^3 ≈ 1674.5 mm^3 (rounded to the nearest tenth)
Therefore, the unused space in the box is the difference between the volume of the container (4000 mm^3) and the total volume of the marbles (1674.5 mm^3):
Unused space = 4000 mm^3 - 1674.5 mm^3 ≈ 2325.5 mm^3 (rounded to the nearest tenth)
Therefore, approximately 2325.5 mm cubed of space in the box is unused.
To calculate the volume of the sculpture, we need to find the difference between the volume of the larger hemisphere and the volume of the smaller hemisphere that was removed.
First, let's find the volume of the larger hemisphere using the formula for a hemisphere: V = (2/3) * π * r^3.
Given that the radius of the larger hemisphere is 20 inches, we can calculate the volume:
V_larger = (2/3) * 3.14 * (20)^3
V_larger ≈ 33500.27 in^3 (rounded to the nearest hundredth)
Next, let's find the volume of the smaller hemisphere:
V_smaller = (2/3) * 3.14 * (15)^3
V_smaller ≈ 5654.6 in^3 (rounded to the nearest tenth)
Finally, we can calculate the volume of the sculpture by subtracting the volume of the smaller hemisphere from the volume of the larger hemisphere:
V_sculpture = V_larger - V_smaller
V_sculpture ≈ 33500.27 in^3 - 5654.6 in^3 ≈ 27845.67 in^3
Therefore, the volume of Kairay's sculpture is approximately 27,846 inches cubed (rounded to the nearest whole number).
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
23.34π yds3
23.34 pi yds cubed
7.2π yds3
7.2 pi yds cubed
7.78π yds3
7.78 pi yds cubed
24.43π 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
113 in.3
113 inches cubed
3,052.1 in.3
3,052.1 inches cubed
381.5 in.3
381.5 inches cubed
190.8 in.3
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
3,900 mm3
3,900 mm cubed
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
19,363 in.3
19,363 inches cubed
7,065 in.3
7,065 inches cubed
9,682 in.3
9,682 inches cubed
16,747 in.3