Fix the mistake: Solid Figures (Volume and Surface Area)
Solid Figures ① Volume and Surface Area of Rectangular Prisms, Prisms, and Cylinders
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
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