Cone Volume Using the Pythagorean Theorem

Hand out the formula reference first, then move from cylinders to cones to spheres. Use the mixed and missing dimension sheets for review before a test.

Find each cone's height from its radius and slant height, then its volume, as with r = 6 and s = 10. The directions on the page read: Use the Pythagorean theorem to find the height h of each cone. Then use V = 1 3 πr²h with 3.14 for π. Round V to the nearest tenth and show your work in the box. An answer key is included.

Yes, both. We made it for 8th grade geometry, and it works the same at home or at school. At home, a student can work through it alone and then go over it with you, which shows quickly what is solid and what needs another look. In class it works as independent practice, homework or a warm-up, and you can print one copy or a full set.

V = ⅓πr²h, one third of the volume of a cylinder with the same base and height. A cone with r = 3 in and h = 5 in has a volume of about 47.1 in³. Volume of Cones, Radius and Height Given has eight cones to practice.

Cube the radius, multiply by π and then by 4/3. If you are given the diameter, halve it first. Volume of Spheres From the Radius mixes radius and diameter problems.

Substitute the volume and the radius into V = πr²h and solve for h. With r = 3 cm and V = 72π cm³, 9πh = 72π, so h = 8 cm. Find a Missing Dimension From the Volume practices this.

It is a solid made of simpler parts, such as a cylinder with a cone on top. Find each part's volume and add them. Volume of Composite Solids With Curves has four such solids.