It seems like you’re looking for help with a math test involving cones, cylinders, and spheres. Here’s a breakdown of the key concepts and how they interrelate:
Key Formulas:
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Volume of a Sphere: \[ V = \frac{4}{3} \pi r^3 \] where \( r \) is the radius of the sphere.
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Volume of a Cylinder: \[ V = \pi r^2 h \] where \( r \) is the radius and \( h \) is the height of the cylinder.
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Volume of a Cone: \[ V = \frac{1}{3} \pi r^2 h \] Similar to the cylinder, but since a cone is one-third the volume of a cylinder with the same base and height.
Relationship:
- Three cones can be combined to form one cylinder. This means: \[ \text{Volume of 3 cones} = \text{Volume of 1 cylinder} \]
Example Calculations:
- If you know the radius or diameter of a shape, you can calculate its volume using the formulas above.
Diameter of a Sphere:
The diameter is double the radius: \[ d = 2r \]
In your notes, you mentioned the diameter of a sphere and referenced \( 300\pi \). If you're dealing with calculations including \( \pi \), remember you can use approximately \( 3.14 \) for \( \pi \).
How to Use the Information:
If you're presented with specific values like \( 1177.5 \) cubic centimeters for a volume or \( 175.8 \) for another measurement, you might need to determine the radius or dimensions based on the volume equations.
For the summary you requested:
- The volume of spheres, cones, and cylinders is essential in understanding their relationships.
- Use the formulas provided for specific calculations.
If you have a specific question about a calculation or need assistance with a certain problem, feel free to ask!
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