The volume of a sphere is given by the formula V = (4/3)*π*r^3, where r is the radius.
Substituting the given radius of 1.8 yards into the formula:
V = (4/3)*π*(1.8)^3
V = (4/3)*π*5.832
V = 7.776π
Rounding to the nearest hundredth:
V ≈ 7.78π yds^3
Therefore, the correct answer is:
7.78π yds^3
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
7.78π yds3
7.78 pi yds cubed
7.2π yds3
7.2 pi yds cubed
23.34π yds3
11 answers
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
3,052.1 in.3
3,052.1 inches cubed
190.8 in.3
190.8 inches cubed
113 in.3
113 inches cubed
381.5 in.3
(1 point)
Responses
3,052.1 in.3
3,052.1 inches cubed
190.8 in.3
190.8 inches cubed
113 in.3
113 inches cubed
381.5 in.3
The volume of a sphere is given by the formula V = (4/3)*π*r^3, where r is the radius.
The radius of the basketball is half its diameter, so the radius would be (9 inches)/2 = 4.5 inches.
Substituting the given radius of 4.5 inches into the volume formula:
V = (4/3)*π*(4.5)^3
V = (4/3)*π*91.125
V = 381.58333π
Rounding to the nearest tenth:
V ≈ 381.5 in^3
Therefore, the correct answer is:
381.5 in^3
The radius of the basketball is half its diameter, so the radius would be (9 inches)/2 = 4.5 inches.
Substituting the given radius of 4.5 inches into the volume formula:
V = (4/3)*π*(4.5)^3
V = (4/3)*π*91.125
V = 381.58333π
Rounding to the nearest tenth:
V ≈ 381.5 in^3
Therefore, the correct answer is:
381.5 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
2,325.3 mm3
2,325.3 mm cubed
3,900 mm3
3,900 mm cubed
33.5 mm3
33.5 mm cubed
1,674.7 mm3
Responses
2,325.3 mm3
2,325.3 mm cubed
3,900 mm3
3,900 mm cubed
33.5 mm3
33.5 mm cubed
1,674.7 mm3
The volume of the marbles can be calculated by finding the volume of one marble and multiplying it by the number of marbles.
The volume of a sphere is given by the formula V = (4/3)*π*r^3, where r is the radius.
Substituting the given radius of 2 mm into the volume formula:
V = (4/3)*π*(2)^3
V = (4/3)*π*8
V = 33.493333...π
Multiplying by the number of marbles:
Total volume of marbles = 33.493333...π * 50 = 1674.666...π
Rounding to the nearest tenth:
Total volume of marbles ≈ 1674.7 mm^3
To find the space unused in the box, subtract the volume of the marbles from the total volume of the container:
Unused space = 4000 mm^3 - 1674.7 mm^3 ≈ 2325.3 mm^3
Therefore, the correct answer is:
2325.3 mm^3
The volume of a sphere is given by the formula V = (4/3)*π*r^3, where r is the radius.
Substituting the given radius of 2 mm into the volume formula:
V = (4/3)*π*(2)^3
V = (4/3)*π*8
V = 33.493333...π
Multiplying by the number of marbles:
Total volume of marbles = 33.493333...π * 50 = 1674.666...π
Rounding to the nearest tenth:
Total volume of marbles ≈ 1674.7 mm^3
To find the space unused in the box, subtract the volume of the marbles from the total volume of the container:
Unused space = 4000 mm^3 - 1674.7 mm^3 ≈ 2325.3 mm^3
Therefore, the correct answer is:
2325.3 mm^3
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
9,682 in.3
9,682 inches cubed
19,363 in.3
19,363 inches cubed
16,747 in.3
Responses
7,065 in.3
7,065 inches cubed
9,682 in.3
9,682 inches cubed
19,363 in.3
19,363 inches cubed
16,747 in.3
To calculate the volume of the sculpture, we need to find the difference in volume between the larger hemisphere with a radius of 20 inches and the smaller hemisphere with a radius of 15 inches.
The volume of a hemisphere is given by the formula V = (2/3)*π*r^3.
For the larger hemisphere with a radius of 20 inches:
V_large = (2/3)*π*(20)^3
V_large = 33529.333...π
For the smaller hemisphere with a radius of 15 inches:
V_small = (2/3)*π*(15)^3
V_small = 14137.5π
Taking the difference of the two volumes:
V_sculpture = V_large - V_small
V_sculpture = 33529.333...π - 14137.5π
V_sculpture = 19391.833...π
Now, rounding the volume to the nearest whole number:
V_sculpture ≈ 19392
Therefore, the correct answer is:
19,392 in^3
The volume of a hemisphere is given by the formula V = (2/3)*π*r^3.
For the larger hemisphere with a radius of 20 inches:
V_large = (2/3)*π*(20)^3
V_large = 33529.333...π
For the smaller hemisphere with a radius of 15 inches:
V_small = (2/3)*π*(15)^3
V_small = 14137.5π
Taking the difference of the two volumes:
V_sculpture = V_large - V_small
V_sculpture = 33529.333...π - 14137.5π
V_sculpture = 19391.833...π
Now, rounding the volume to the nearest whole number:
V_sculpture ≈ 19392
Therefore, the correct answer is:
19,392 in^3
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Suppose a sphere, cylinder, and cone all share the same radius. The cylinder and cone also share the same height, which is twice the radius. Which of the following is true about the relationship between the volume formulas for the sphere, cylinder, and cone?(1 point)
Responses
cylinder = sphere – cone
cylinder = sphere – cone
sphere = cylinder + cone
sphere = cylinder + cone
cone = cylinder – sphere
cone = cylinder – sphere
cone = sphere – cylinder
Responses
cylinder = sphere – cone
cylinder = sphere – cone
sphere = cylinder + cone
sphere = cylinder + cone
cone = cylinder – sphere
cone = cylinder – sphere
cone = sphere – cylinder
The correct relationship between the volume formulas for the sphere, cylinder, and cone in this case is:
sphere = cylinder + cone
The volume formula for a sphere is V_sphere = (4/3) * π * r^3, where r is the radius.
The volume formula for a cylinder is V_cylinder = π * r^2 * h, where r is the radius and h is the height.
The volume formula for a cone is V_cone = (1/3) * π * r^2 * h, where r is the radius and h is the height.
Since in this case the cylinder and cone share the same height (which is twice the radius), we can substitute 2r for h in the volume formulas for the cylinder and cone:
V_cylinder = π * r^2 * (2r) = 2π * r^3
V_cone = (1/3) * π * r^2 * (2r) = (2/3) * π * r^3
Adding these two volumes together, we get:
V_cylinder + V_cone = 2π * r^3 + (2/3) * π * r^3 = (8/3) * π * r^3
This is equal to the volume of the sphere:
V_sphere = (4/3) * π * r^3
So, the correct relationship is:
sphere = cylinder + cone
sphere = cylinder + cone
The volume formula for a sphere is V_sphere = (4/3) * π * r^3, where r is the radius.
The volume formula for a cylinder is V_cylinder = π * r^2 * h, where r is the radius and h is the height.
The volume formula for a cone is V_cone = (1/3) * π * r^2 * h, where r is the radius and h is the height.
Since in this case the cylinder and cone share the same height (which is twice the radius), we can substitute 2r for h in the volume formulas for the cylinder and cone:
V_cylinder = π * r^2 * (2r) = 2π * r^3
V_cone = (1/3) * π * r^2 * (2r) = (2/3) * π * r^3
Adding these two volumes together, we get:
V_cylinder + V_cone = 2π * r^3 + (2/3) * π * r^3 = (8/3) * π * r^3
This is equal to the volume of the sphere:
V_sphere = (4/3) * π * r^3
So, the correct relationship is:
sphere = cylinder + cone
3 answers