Chapter 17
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Chapter 17: Surface Area and Volume
17.1 Surface Area of 3D Shapes
Surface area is the total area covered by all the faces of a 3D object. It is measured in square units (cm², m²).
Common Surface Area Formulas:
Cube: 6s26s^26s2 (since all 6 faces are squares)
Rectangular Prism: 2lw+2lh+2wh2lw + 2lh + 2wh2lw+2lh+2wh
Sphere: 4πr24pi r^24πr2
Example:
A cube has side length 5 cm. The surface area is:
6(52)=6(25)=150 cm26(5^2) = 6(25) = 150 text{ cm}^26(52)=6(25)=150 cm2
17.2 Volume of 3D Shapes
Volume measures how much space an object takes up and is measured in cubic units (cm³, m³).
Common Volume Formulas:
Cube: s3s^3s3
Rectangular Prism: lwhlwhlwh
Sphere: 43πr3frac{4}{3} pi r^334πr3
Example:
A box with dimensions 4 cm × 3 cm × 6 cm has a volume of:
4×3×6=72 cm34 times 3 times 6 = 72 text{ cm}^34×3×6=72 cm3
Real-World Applications:
Understanding surface area and volume is important for architecture, packaging, and engineering.
Exercises
Find the surface area of a cube with a side length of 7 cm.
A water tank is 10 m long, 4 m wide, and 3 m high. Find its volume.
Find the volume of a sphere with a radius of 5 cm.
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