A cylinder has radius 3 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 example, we have a cylinder with a radius of 3 centimeters and a height of 10 centimeters. These measurements are key to calculating its volume.
To find the volume of a cylinder, we first calculate the area of its circular base using the formula A equals pi times radius squared. With a radius of 3 centimeters, the base area is pi times 3 squared, which equals 9 pi square centimeters. The volume is then found by multiplying this base area by the height of the cylinder, giving us the formula V equals pi times radius squared times height.
Now we'll calculate the volume using the formula. First, we write V equals pi times r squared times h. Substituting our values, we get V equals pi times 3 squared times 10. This simplifies to pi times 9 times 10. Multiplying these together gives us 90 pi cubic centimeters. Converting to a decimal approximation, this is approximately 282.74 cubic centimeters.
To visualize the volume calculation, imagine stacking circular disks of area 9 pi square centimeters. We stack 10 of these disks, each representing a unit of height. This stacking process demonstrates how the volume is the base area multiplied by the height, giving us our final volume of 90 pi cubic centimeters.
To summarize, we found the volume of a cylinder with radius 3 centimeters and height 10 centimeters. Using the formula V equals pi times radius squared times height, we calculated the volume to be exactly 90 pi cubic centimeters, which is approximately 282.74 cubic centimeters. This demonstrates the fundamental principle that cylinder volume always equals the base area multiplied by the height.