The diameter of a sphere (1 point)
• is the distance from the center of the sphere to any point on the surface of the sphere.
• is the longest distance on a sphere.
is half the length of the radius.
• does not pass through the center of the sphere.
5 answers
• is half the length of the radius.
Find the volume of a sphere with a radius 1.1 ft. Use 3.14 as an approximation for pi. Round your answer to the nearest hundredth, if necessary. (1 point)
• 15.2 ft.3
• 16.72 ft.3
• 5.57 ft.3
• 13.82 it.
• 15.2 ft.3
• 16.72 ft.3
• 5.57 ft.3
• 13.82 it.
To find the volume of a sphere, we can use the formula: V = (4/3) * pi * r^3.
Given that the radius (r) is 1.1 ft and using 3.14 as an approximation for pi, we can substitute the values into the formula.
V = (4/3) * 3.14 * (1.1^3)
V = (4/3) * 3.14 * 1.331
V ≈ 5.57 ft^3
Therefore, the correct answer is:
• 5.57 ft^3
Given that the radius (r) is 1.1 ft and using 3.14 as an approximation for pi, we can substitute the values into the formula.
V = (4/3) * 3.14 * (1.1^3)
V = (4/3) * 3.14 * 1.331
V ≈ 5.57 ft^3
Therefore, the correct answer is:
• 5.57 ft^3
Suppose a sphere, cylinder, and cone all share the same radius and 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)
• 1 cylinder = 2 cones + 1 sphere
• sphere - cone = cylinder
• 3 cones = 1 cylinder
• sphere = cylinder + cone
(1 point)
• 1 cylinder = 2 cones + 1 sphere
• sphere - cone = cylinder
• 3 cones = 1 cylinder
• sphere = cylinder + cone
The correct relationship between the volume formulas for the sphere, cylinder, and cone, given the provided conditions, is:
• sphere = cylinder + cone
Since the radius and height are the same for the cylinder and cone, we can express their volumes as:
Cylinder volume = π * r^2 * h
Cone volume = (1/3) * π * r^2 * h
Substituting the height value of the cone, which is twice the radius, we get:
Cylinder volume = π * r^2 * (2r)
Cone volume = (1/3) * π * r^2 * (2r)
Simplifying the expressions:
Cylinder volume = 2π * r^3
Cone volume = (2/3)π * r^3
Adding the volumes of the cylinder and cone:
Cylinder + Cone volume = 2π * r^3 + (2/3)π * r^3
Cylinder + Cone volume = (6/3)π * r^3 + (2/3)π * r^3
Cylinder + Cone volume = (8/3)π * r^3
This is equal to the volume of the sphere:
Sphere volume = (4/3)π * r^3
Therefore, we can conclude that:
• sphere = cylinder + cone
• sphere = cylinder + cone
Since the radius and height are the same for the cylinder and cone, we can express their volumes as:
Cylinder volume = π * r^2 * h
Cone volume = (1/3) * π * r^2 * h
Substituting the height value of the cone, which is twice the radius, we get:
Cylinder volume = π * r^2 * (2r)
Cone volume = (1/3) * π * r^2 * (2r)
Simplifying the expressions:
Cylinder volume = 2π * r^3
Cone volume = (2/3)π * r^3
Adding the volumes of the cylinder and cone:
Cylinder + Cone volume = 2π * r^3 + (2/3)π * r^3
Cylinder + Cone volume = (6/3)π * r^3 + (2/3)π * r^3
Cylinder + Cone volume = (8/3)π * r^3
This is equal to the volume of the sphere:
Sphere volume = (4/3)π * r^3
Therefore, we can conclude that:
• sphere = cylinder + cone
1 answer