Volume of a Cone

These objects all have one thing in common; they're cones! But how much space is inside? We can find out by finding the 'volume of a cone'. A cone is a three-dimensional shape made from a circular base and a curved surface that ends in a point. To calculate this, we will use the formula volume equals one-third, times pi, times the radius squared, times the height. The radius is the distance from the center of the circular base to the outside. The height is the vertical distance between the center of the base to the tip of the cone. Time to look at an actual cone and find its volume. Find the volume of the cone, and round your answer to the nearest tenth of a centimeter. First, write the formula you are using to find the volume. V equals one-third, pi, r squared, h. Next, let's identify the radius and height of the cone. The radius, or r equals four centimeters. The height, or h is equal to nine centimeters. These values can be substituted into the formula. First multiply the numbers we know, leaving pi for the end. One-third times four squared, times nine, is equal to forty-eight. Remember, pi is approximately three point one four and so on, and we will use a calculator to help us find the volume. The product of forty-eight and pi is approximately one hundred fifty and eight tenths. We always represent volume with cubic units. The volume of the cone is approximately one hundred fifty and eight-tenths centimeters cubed. Let's try another example! Find the volume of the cone, and round your answer to the nearest tenth of an inch. Starting with our formula, the radius for this cone is three inches and the height is five, which we substitute in the formula. Leaving pi for the last step, the product of one-third, three-squared, and five is fifteen. Fifteen multiplied by pi is approximately forty-seven and one-tenth. And don't forget to include the units in your final answer! Let's try one more, but this time find the volume of the cone in terms of pi. This means that we will not be calculating pi on our calculator, but rather leaving pi as a symbol in our final answer. Start by writing down the formula, and then ask yourself, what are the radius and height? The radius is six centimeters, and the height is twelve. Pause the video here and rewrite the formula for volume including the known values. Your formula now should look like this! To find the final solution in terms of pi, we will calculate all but the pi in our calculators. The volume equals one hundred forty-four, pi, centimeters cubed, which is an exact measurement since it was not rounded. Let's wrap this all up! This is the formula used to find the volume of a cone. The r is the radius, and h is the height of the cone. Using the formula, substitute in any known values, solve, and be sure to always include your cubic units. Stay calm, don't get cone-fused and you can find the volume of these 3D shapes with ease!