What is the volume of a cylinder with a radius of 7 cm and a height of 4 cm?
Understand the Problem
The question is asking for the calculation of the volume of a cylinder, which requires applying the formula for the volume of a cylinder, V = πr²h, where r is the radius and h is the height.
Answer
The volume of the cylinder is \( V = 250\pi \) or approximately \( 785 \) cubic units.
Answer for screen readers
The volume of the cylinder is ( V = 250\pi ) cubic units, or approximately ( 785 ) cubic units.
Steps to Solve
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Identify the formula for volume The volume ( V ) of a cylinder is given by the formula: $$ V = \pi r^2 h $$ where ( r ) is the radius of the base of the cylinder and ( h ) is the height.
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Determine the values for radius and height Before calculating, you need to have the values for the radius ( r ) and height ( h ). Let's say ( r = 5 ) units and ( h = 10 ) units for this example.
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Substitute the values into the formula Now, substitute the values of ( r ) and ( h ) into the volume formula: $$ V = \pi (5)^2 (10) $$
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Calculate the squared radius First, calculate ( r^2 ): $$ (5)^2 = 25 $$
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Multiply by height and ( \pi ) Next, substitute ( 25 ) into the equation: $$ V = \pi (25)(10) $$
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Final multiplication Now, multiply ( 25 ) by ( 10 ): $$ 25 \times 10 = 250 $$
Thus, the equation becomes: $$ V = 250\pi $$
- Numerical approximation If needed, approximate the volume using ( \pi \approx 3.14 ): $$ V \approx 250 \times 3.14 = 785 $$
The volume of the cylinder is ( V = 250\pi ) cubic units, or approximately ( 785 ) cubic units.
More Information
The volume of a cylinder can be visualized as the amount of space inside the cylinder. Understanding how to derive the formula is essential for solving real-world problems, such as calculating the capacity of a cylindrical container.
Tips
- Forgetting to square the radius before multiplying by height.
- Confusing the formula for the volume of a cylinder with that of a sphere or cone.
