Volume word problems — Basic example

- [Instructor] Let's Scream for Ice Cream serves three scoops of ice cream in its signature cone, and they draw a picture of it right over here. Each scoop is a sphere with a radius four centimeters, or with a radius of four centimeters. What is the total volume of ice cream served per cone to the nearest cubic centimeter? They want us to use pi as being approximately 3.14. We know that it's not exactly 3.14. It's 3.14159 and just keeps going on and on and on forever. Some people memorize thousands of digits, thousands of digits of pi, and even that's just a, there's an infinite number of digits to pi. But anyway, let's see if we can tackle this. So there's three scoops of ice cream. Each of them is a sphere, so this bottom one you can't fully see because it's into the cone. They each have a radius of four centimeters, so if you go from the center of the sphere to the surface of the sphere, that is four centimeters. So what we really just need to do is figure out the volume of one of these spheres, one of these scoops, and then multiply by three because we have three scoops and they all have a radius of four centimeters. They all have the same volume. To do that, we have to remember the formula for the volume of a sphere. The formula for the volume of a sphere is volume is equal to 4/3 pi r cubed, where r is the radius of the sphere, in this case it's going to be four centimeters, and pi is pi, the famous number, the ratio between the circumference and the diameter of a circle, and we're going to say, for the sake of this exercise, we're going to say it's 3.14, but a lot of calculators can get a much more precise representation of pi, but we're just going to use 3.14 because that's what they told us to do. So the volume of one, the volume of one sphere is going to be 4/3 times, we're going to use 3.14, 3.14 for pi, times the radius cubed. The radius is four centimeters, and we are going to cube it. If you do four centimeters and then you cube it, you're going to get the units centimeters cubed, or cubic centimeters. Actually, let me just do that. Four centimeters cubed. So this is going to be the volume of one of our spheres, and then we have three of them, so let's multiply to get the volume of all of them combined. Let's multiply this times three, and it actually makes our calculation a little bit simpler, because you have three divided by three, and so we are left with, we are left with four times 3.14. If we were more precise, we would just say this is pi right over here, this is just an approximation for pi, and then four centimeters cubed. Let's see, four cubed is 16 times four, it's 64, so this is going to be times 64, and you could also think of this as cubing the dimension, so centimeters cubed, that's going to be cubic centimeters. So it's going to be this many cubic centimeters. So let's think about it. This is going to be, we could do this by hand. Four times 64, that is 256. So it's going to be 3.14 times 256 cubic centimeters. But we're allowed to use a calculator for this one, so let's just take our calculator out and let's just multiply it out. 3.14 times 256 is equal to 803.84, and they tell us to round to the nearest cubic centimeter. So 803.84 cubic centimeters, we round to the nearest centimeter, or we round to the nearest cubic centimeter, we'll round up because we have an eight right here, so this is going to be 804 cubic centimeters. So this is approximately 804 cubic, 804 cubic centimeters. That is the volume of these three spheres combined.