How do you find the volume inside the cylinder but outside the sphere, given that the height \( H \) of the cylinder is [tex]12 \, \text{cm}[/tex]?
Answer (2)
To find the volume inside the cylinder but outside the sphere, you first need to calculate the volume of the cylinder and sphere separately. The volume of a cylinder is given by the formula V = πr²h, where r is the radius of the base and h is the height. The volume of a sphere is given by the formula V = (4/3)πr³, where r is the radius of the sphere.
Once you have the volumes of the cylinder and sphere, subtract the volume of the sphere from the volume of the cylinder to find the volume inside the cylinder but outside the sphere.
For example, if the height of the cylinder is 12 cm, you would calculate the volumes as follows:
Volume of cylinder: V = πr²h = 3.142 × (radius)² × 12
Volume of sphere: V = (4/3)πr³ = (4/3) × 3.142 × (radius)³
Volume inside the cylinder but outside the sphere: Volume of cylinder - Volume of sphere
To find the volume inside the cylinder but outside the sphere, calculate the volume of both shapes separately using their respective formulas and then subtract the sphere's volume from the cylinder's volume. The volume of a cylinder is given by V cy l in d er = π r cy l in d er 2 h , and the volume of a sphere is V s p h ere = 3 4 π r s p h ere 3 . Finally, ensure you have the correct radii to perform these calculations.
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