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Questions and Answers
What is the correct volume of the cylinder shown?
What is the correct volume of the cylinder shown?
What is the correct radius of the sphere with a volume of $4,500π$ cubic inches?
What is the correct radius of the sphere with a volume of $4,500π$ cubic inches?
What is the correct length of the slant height of the cone with a volume of $240π$ cubic meters and a height of 5 meters?
What is the correct length of the slant height of the cone with a volume of $240π$ cubic meters and a height of 5 meters?
Which cylinder is taller between Cylinder A with a radius of 13 inches and Cylinder B with a radius of 10 inches?
Which cylinder is taller between Cylinder A with a radius of 13 inches and Cylinder B with a radius of 10 inches?
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Why is a unit sphere not a good unit of volume measurement for all spheres?
Why is a unit sphere not a good unit of volume measurement for all spheres?
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In which scenario would the radius be the most difficult to find?
In which scenario would the radius be the most difficult to find?
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What is the relationship between the volume of a cylinder and its radius?
What is the relationship between the volume of a cylinder and its radius?
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If a sphere has a volume of 4,500π cubic yards, what would be the approximate diameter of the sphere?
If a sphere has a volume of 4,500π cubic yards, what would be the approximate diameter of the sphere?
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How does changing the diameter of a mug while keeping its height constant affect the volume it can hold?
How does changing the diameter of a mug while keeping its height constant affect the volume it can hold?
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What is the general relationship between the radius and height in cylinders?
What is the general relationship between the radius and height in cylinders?
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If a cone has a volume of 735π cubic millimeters and a height of 5 millimeters, what would be a plausible radius for this cone?
If a cone has a volume of 735π cubic millimeters and a height of 5 millimeters, what would be a plausible radius for this cone?
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Study Notes
Volume of 3D Shapes
- The volume of a cylinder can be found by calculating the area of its base (πr^2) and multiplying it by its height (h).
Spheres
- A sphere with a volume of 4,500π cubic inches has a radius that can be found by rearranging the formula for the volume of a sphere (V = (4/3)πr^3).
- A unit sphere is not a good unit of volume measurement for all spheres because spheres come in different sizes.
Cones
- The volume of a cone can be found by calculating the area of its base (πr^2) and multiplying it by its height (h) divided by 3.
- If a cone has a volume of 240π cubic meters and a height of 5 meters, its radius can be found by rearranging the formula for the volume of a cone.
- If a cone has a volume of 735π cubic millimeters and a height of 5 millimeters, its radius can be found by rearranging the formula for the volume of a cone.
Cylinders
- The radius of a cylinder affects its volume, with a larger radius resulting in a greater volume.
- If a cylinder has a radius of 13 inches and another cylinder has a radius of 10 inches, the taller cylinder will be the one with the larger radius.
- If the diameter of a mug is increased while keeping its height constant, its volume will increase.
- The general relationship between the radius and height in cylinders is that as the radius increases, the volume increases, and as the height increases, the volume also increases.
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Description
Practice finding missing dimensions in geometric shapes like cylinders and cones. Calculate the height or radius based on the given volume and one of the dimensions. Examples involve both cylinders and cones of different measurements.
