Volume of the solid made by one full turn?
A hard-level "Volume" problem.For a solid of revolution, "the farthest point from the axis is the radius". Spin a rectangle and you get a cylinder, a right triangle a cone, a semicircle a sphere.
GivenThe right triangle is spun once around the dashed axis / π = 3.14
Hints
- First picture the triangle part-way through the turn, sweeping around the axis.
- After a full turn, the path swept by the slanted side becomes a smooth surface and the bottom becomes a circle: the solid is a cone.
- The base circle's radius is the distance from the axis to the farthest point — that is, the horizontal side, 5 cm.
- The height is the side along the axis, 12 cm. Base and height are both known now.
- A cone is "base area × height ÷ 3": 5 × 5 × 3.14 × 12 ÷ 3
Answer 314cm³
More "Volume" problems
- What is the volume of the bottom part?
- What is the volume of the solid produced?
- Volume of the stone?
- Volume of the cuboid?
- What is the volume of the box?
- Volume of the cylinder?