Calculating dimensions of a cone
About this video
A cone has volume 50 pi cubic centimeters and a diameter of 10 cm. Sal uses V = 1/3 pi r^2 h, halves the diameter to get radius 5 (so r^2 = 25), and divides both sides by 1/3 x pi x 25 to find the height is 6 cm.
You'll be able to
- write the volume of a cone as 1/3 x pi r^2 x h.
- find the radius from a diameter before using the formula.
- solve for the height of a cone given its volume.
Key words
- cone
- A 3D shape with a circular base that narrows to a point.
- diameter
- The distance across a circle through its center; twice the radius.
- radius
- Half the diameter: the distance from the center to the edge of a circle.
Transcript
- [Instructor] The volume of the cone is 50 Pi cubic centimeters. Find the height of the cone. Pause this video, have a go at that. All right, let's just remind ourselves the volume of a cone. The volume of a cone is 1/3 times the area of the base, which is Pi R squared, times the height.
So let's see what we know. We know what the volume is. It's 50 Pi cubic centimeters, so I'll write that here. 50 Pi and times 1/3, or it's equal to 1/3 times Pi. What's our radius squared? Well, they're not giving us the radius here. They're giving us the diameter.
So the radius is going to be half of that. This right over here is five centimeters. So the radius squared is going to be 25, and then all of that times H. So if we want to solve for H, we would just divide both sides of this equation by all of this, by all of this business over here.
We would divide by 1/3 Pi times 25. Let me write times 25. We would also do it here, 1/3 times Pi times 25. Of course, that all cancels out with that. The Pi cancels out with Pi. Let's see, 50 divided by 25 is two. So this is two, this is a one. And all we're left with is two divided by 1/3.
That's the same thing as two times three. So that's going to be six on the left-hand side is equal to H. So the height of the cone, six centimeters, and we're done.
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