Let us look at the formulas for the volume and surface area of solid figures shaped like columns (rectangular prisms, prisms, and cylinders).
Formulas for Column-Shaped Solid Figures
- Volume = base area (the area of one bottom face) × height
- Surface area = base area × 2 + lateral area (the area of the side faces)
- Lateral area of a cylinder = circumference of the circle × height = 2 × π × r × h
Example 1 (Rectangular Prism): Find the volume and surface area of a rectangular prism with a length of 4 cm, a width of 5 cm, and a height of 3 cm.
Solution:
① Volume = 4 × 5 × 3 = 60 cm³
② Surface area = 2 × (4×5 + 5×3 + 4×3) = 2 × (20 + 15 + 12) = 2 × 47 = 94 cm²
Solution:
① Volume = 4 × 5 × 3 = 60 cm³
② Surface area = 2 × (4×5 + 5×3 + 4×3) = 2 × (20 + 15 + 12) = 2 × 47 = 94 cm²
Example 2 (Cylinder): Find the volume and surface area of a cylinder with a base radius of 3 cm and a height of 5 cm. (π = 3.14)
Solution:
① Volume = 3² × 3.14 × 5 = 9 × 3.14 × 5 = 141.3 cm³
② Two bases = 2 × 9 × 3.14 = 56.52
③ Lateral area = 2 × 3 × 3.14 × 5 = 94.2
④ Surface area = 56.52 + 94.2 = 150.72 cm²
Solution:
① Volume = 3² × 3.14 × 5 = 9 × 3.14 × 5 = 141.3 cm³
② Two bases = 2 × 9 × 3.14 = 56.52
③ Lateral area = 2 × 3 × 3.14 × 5 = 94.2
④ Surface area = 56.52 + 94.2 = 150.72 cm²