Surface Areas and Volumes Notes: Class 9 Maths Chapter 13
Class 9 Maths Chapter 13 Surface Areas and Volumes covers the formulas for the surface area and volume of a cuboid, cube, cylinder, cone, sphere and hemisphere.
Overview of Topics & Subtopics (Click to Jump)
1. Cuboid and Cube
Short Note:
• Cuboid (length l, breadth b, height h): Total Surface Area = 2(lb + bh + hl); Volume = l × b × h.
• Cube (edge a): Total Surface Area = 6a²; Volume = a³.
2. Cylinder and Cone
Short Note:
• Right Circular Cylinder (radius r, height h): Curved Surface Area = 2πrh; Total Surface Area = 2πr(r + h); Volume = πr²h.
• Right Circular Cone (radius r, height h, slant height l = √(r²+h²)): Curved Surface Area = πrl; Total Surface Area = πr(l + r); Volume = ⅓πr²h.
3. Sphere and Hemisphere
Short Note:
• Sphere (radius r): Surface Area = 4πr²; Volume = &frac43;πr³.
• Hemisphere (radius r): Curved Surface Area = 2πr²; Total Surface Area = 3πr²; Volume = ⅔πr³.
NCERT Textbook Exercise Questions
A matchbox measures 4 cm × 2.5 cm × 1.5 cm. Find the volume of a packet containing 12 such matchboxes.
Answer: Volume of one matchbox = 4 × 2.5 × 1.5 = 15 cm³. Volume of 12 matchboxes = 12 × 15 = 180 cm³.
The curved surface area of a right circular cylinder of height 14 cm is 88 cm². Find the diameter of the base of the cylinder.
Answer: 2πrh = 88 ⇒ 2 × 22/7 × r × 14 = 88 ⇒ r = 88 × 7 / (2 × 22 × 14) = 1 cm. So diameter = 2 cm.
Find the volume of a right circular cone with radius 6 cm and height 7 cm.
Answer: Volume = ⅓πr²h = ⅓ × 22/7 × 36 × 7 = 264 cm³.
Find the surface area of a sphere of radius 7 cm.
Answer: Surface Area = 4πr² = 4 × 22/7 × 49 = 616 cm².
A hemispherical bowl made of steel is 0.25 cm thick; the inner radius of the bowl is 5 cm. Find the outer curved surface area of the bowl.
Answer: Outer radius = inner radius + thickness = 5 + 0.25 = 5.25 cm. Curved Surface Area = 2πr² = 2 × 22/7 × 5.25² ≈ 173.25 cm².
