Volume of the cone?

A normal-level "Volume" problem.Any pointed solid is one third of the prism with the same base and height — pyramids and cones alike.

GivenBase radius 6 cm / height 10 cm / π = 3.14

Hints

1. A cone also starts from "base area × height". Begin with the area of the base circle.
2. The radius is 6 cm, so 6 × 6 × 3.14 = 113.04 cm².
3. Now sketch, in dashed lines, the cylinder with the same base and the same height. The cone fits snugly inside it.
4. The cylinder holds 113.04 × 10 = 1130.4 cm³. So what fraction of it is the cone?
5. Fill the cone with water and pour it into the cylinder: it takes exactly three coneloads to fill it. The pointed shape loses exactly two thirds.
6. So the answer is 113.04 × 10 ÷ 3.

Answer 376.8cm³

More "Volume" problems

• What is the volume of the bottom part?
• Volume of the solid made by one full turn?
• What is the volume of the solid produced?
• Volume of the stone?
• Volume of the cuboid?
• What is the volume of the box?

Browse by idea

• Flatten the solid before you think about it
• Back to why the formula works

Volume Problems (8)　Standard Problems (42)

See all 100 problems