8th Grade Mathematics
Volume and Surface Area of Cylinders, Cones, and Spheres
#### Cylinders
**Volume of a Cylinder**
- **Formula**: \( V = \pi r^2 h \)
- **Explanation**:
- \( r \) is the radius of the base of the cylinder.
- \( h \) is the height of the cylinder.
- The volume is the area of the base (\(\pi r^2\)) multiplied by the height.
**Surface Area of a Cylinder**
- **Formula**: \( SA = 2\pi r(h + r) \)
- **Explanation**:
- The surface area consists of two parts: the area of the two circular bases and the area of the
rectangular side (the label of the can).
- \( 2\pi r^2 \) accounts for the area of the two bases.
- \( 2\pi rh \) accounts for the area of the side (the circumference of the base times the height).
#### Cones
**Volume of a Cone**
- **Formula**: \( V = \frac{1}{3}\pi r^2 h \)
- **Explanation**:
- \( r \) is the radius of the base of the cone.
- \( h \) is the height of the cone (the perpendicular distance from the base to the apex).
- The volume is one-third the volume of a cylinder with the same base and height.
