A cylinder has radius 3 cm and height 11 cm. What is the volume
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The volume of a cylinder is calculated using the formula V equals pi times r squared times h. In this formula, V represents the volume, pi is the mathematical constant approximately equal to 3.14159, r is the radius of the circular base, and h is the height of the cylinder.
Now let's visualize the cylinder with the given dimensions. We have a radius of 3 centimeters and a height of 11 centimeters. In this 2D representation, the curved surface is shown as a rectangle, with the circular bases represented as ellipses. The red line shows the radius of 3 centimeters, and the blue line shows the height of 11 centimeters.
Now we substitute the known values into the volume formula. We replace r with 3 and h with 11, giving us V equals pi times 3 squared times 11.
Let's calculate the volume step by step. First, we calculate 3 squared, which equals 9. Next, we multiply 9 by 11, which gives us 99. Finally, we multiply by pi, resulting in 99 pi cubic centimeters.
The final answer can be expressed in two forms. The exact answer is 99 pi cubic centimeters. For an approximate decimal value, we substitute pi with 3.14159 and multiply by 99, which gives us approximately 311.02 cubic centimeters.
Let's summarize the complete solution. We were given a cylinder with radius 3 centimeters and height 11 centimeters. Using the formula V equals pi r squared h, we substituted the values to get V equals pi times 3 squared times 11. This simplified to 99 pi cubic centimeters, which is approximately 311.02 cubic centimeters.