A cylinder has radius 4 cm and height 10 cm. What is the volume
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A cylinder is a three-dimensional shape with two parallel circular bases connected by a curved surface. In this problem, we are given a cylinder with a radius of 4 centimeters and a height of 10 centimeters. Our goal is to find the volume of this cylinder.
To find the volume of a cylinder, we start with the area of its circular base. The area of a circle is given by the formula pi times radius squared. When we extend this two-dimensional area through the height of the cylinder, we get the three-dimensional volume. This gives us the formula: Volume equals pi times radius squared times height.
Let's substitute our given values into the volume formula. We have radius equals 4 centimeters and height equals 10 centimeters. First, we square the radius: 4 squared equals 16. Then we multiply by pi and by the height: 16 times pi times 10 equals 160 pi cubic centimeters. This is the exact answer. For a decimal approximation, we use pi approximately equals 3.14159, giving us about 502.65 cubic centimeters.
Here's our cylinder with the calculated volume. The radius is 4 centimeters and the height is 10 centimeters. The volume of 160 pi cubic centimeters (approximately 502.65 cubic centimeters) represents the amount of space inside this cylinder. To put this in perspective, this volume is roughly equivalent to about half a liter of liquid, which is about the size of a standard water bottle.
Let's practice with another example. Suppose we have a cylinder with a radius of 3 centimeters and a height of 7 centimeters. Using the same formula, volume equals pi times radius squared times height, we substitute our values. Three squared is 9, and 9 times 7 is 63. So the volume is 63 pi cubic centimeters, or approximately 197.92 cubic centimeters. This demonstrates how the same method applies to any cylinder, regardless of its specific dimensions.