A cylinder has radius 4 cm and height 12 cm. What is the volume
视频信息
答案文本
视频字幕
A cylinder is a three-dimensional shape with two parallel circular bases connected by a curved surface. In this example, we have a cylinder with a radius of 4 centimeters and a height of 12 centimeters. These are the two key measurements we need to calculate its volume.
To understand the volume formula for a cylinder, let's think of it as stacking many circular disks on top of each other. The volume is simply the area of one circular base multiplied by the height. Since the area of a circle is pi times radius squared, the volume of a cylinder is pi times radius squared times height.
Now we'll substitute our given values into the volume formula. We have radius equals 4 centimeters and height equals 12 centimeters. So we replace r with 4 and h with 12 in our formula V equals pi r squared h. This gives us V equals pi times 4 squared times 12.
Let's calculate the volume step by step. First, we multiply 16 by 12 to get 192. So our volume is 192 pi cubic centimeters. This is the exact answer. To get the approximate decimal value, we multiply 192 by pi, which is approximately 3.14159. This gives us approximately 603.19 cubic centimeters.
Let's review our complete solution. We were given a cylinder with radius 4 centimeters and height 12 centimeters. Using the formula V equals pi r squared h, we substituted our values and calculated V equals 192 pi cubic centimeters, which is approximately 603.19 cubic centimeters. This answer makes sense because a cylinder with these dimensions should have a substantial volume, and our calculated value is reasonable for the given measurements.