Surface Areas and Volumes — Class 9 Mathematics NCERT Solutions (Free)

Free step-by-step NCERT solutions for Class 9 Mathematics chapter "Surface Areas and Volumes" — 8 important questions with detailed answers for CBSE board exam preparation.

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TL;DR: Free step-by-step NCERT solutions for Class 9 Mathematics chapter "Surface Areas and Volumes" — 8 important questions with detailed answers for CBSE b…

Written & reviewed by the Syllab.in Academic Team (CBSE/NCERT subject experts) · Updated Jul 23, 2026

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Key Questions Covered:

Find the total surface area and volume of a cuboid (rectangular prism) with l…
A cylinder has radius 7 cm and height 10 cm. Find its curved surface area, to…
A cone has base radius 5 cm, height 12 cm. Find the slant height, curved surf…
A sphere has radius 6 cm. Find its surface area and volume.
A hemisphere has radius 8 cm. Find its curved surface area, total surface are…
A cube has side length 5 cm. Find its total surface area, lateral surface are…
+ 2 more questions in the full chapter

Solutions Summary:

Question	Status
Find the total surface area and volume of a cuboid (recta…	✓ Solved
A cylinder has radius 7 cm and height 10 cm. Find its cur…	✓ Solved
A cone has base radius 5 cm, height 12 cm. Find the slant…	✓ Solved
A sphere has radius 6 cm. Find its surface area and volume.	✓ Solved
A hemisphere has radius 8 cm. Find its curved surface are…	✓ Solved
A cube has side length 5 cm. Find its total surface area,…	✓ Solved

Showing 6 of 8 questions

Q1: Find the total surface area and volume of a cuboid (rectangular prism) with length 12 cm, breadth 8 cm, and height 6 cm.

Step 1: Cuboid dimensions: Length (l) = 12 cm Breadth (b) = 8 cm Height (h) = 6 cm Step 2: Total Surface Area of Cuboid: Formula: Total Surface Area = 2(lb + bh + hl) Step 3: Calculate each product: lb = 12 × 8 = 96 cm² bh = 8 × 6 = 48 cm² hl = 6 × 12 = 72 cm² Step 4: Sum of products: lb + bh + hl = 96 + 48 + 72 = 216 cm² Step 5: Calculate surface area: Total Surface Area = 2 × 216 = 432 cm² Step 6: Volume of Cuboid: Formula: Volume = l × b × h Volume = 12 × 8 × 6 Volume = 96 × 6 Volume = 5...

Q2: A cylinder has radius 7 cm and height 10 cm. Find its curved surface area, total surface area, and volume.

Step 1: Cylinder dimensions: Radius (r) = 7 cm Height (h) = 10 cm Step 2: Curved Surface Area (Lateral Surface Area): Formula: Curved Surface Area = 2πrh Curved Surface Area = 2 × π × 7 × 10 Curved Surface Area = 140π cm² Curved Surface Area ≈ 140 × 3.14159 ≈ 439.82 cm² Step 3: Area of Two Circular Bases: Area of one circle = πr² Area of one circle = π × 7² Area of one circle = 49π cm² Area of two circles = 2 × 49π = 98π cm² Area of two circles ≈ 98 × 3.14159 ≈ 307.88 cm² Step 4: Total Surfac...

Q3: A cone has base radius 5 cm, height 12 cm. Find the slant height, curved surface area, total surface area, and volume.

Step 1: Cone dimensions: Base radius (r) = 5 cm Height (h) = 12 cm Slant height (l) = ? Step 2: Find slant height using Pythagoras theorem: The slant height, radius, and height form a right triangle. l² = r² + h² l² = 5² + 12² l² = 25 + 144 l² = 169 l = 13 cm Step 3: Curved Surface Area (Lateral Surface Area): Formula: Curved Surface Area = πrl Curved Surface Area = π × 5 × 13 Curved Surface Area = 65π cm² Curved Surface Area ≈ 65 × 3.14159 ≈ 204.20 cm² Step 4: Area of Circular Base: Area of ...

Q4: A sphere has radius 6 cm. Find its surface area and volume.

Step 1: Sphere radius: r = 6 cm Step 2: Surface Area of Sphere: Formula: Surface Area = 4πr² Surface Area = 4 × π × 6² Surface Area = 4 × π × 36 Surface Area = 144π cm² Surface Area ≈ 144 × 3.14159 ≈ 452.39 cm² Step 3: Volume of Sphere: Formula: Volume = (4/3)πr³ Volume = (4/3) × π × 6³ Volume = (4/3) × π × 216 Volume = (4/3 × 216) × π Volume = (864/3) × π Volume = 288π cm³ Volume ≈ 288 × 3.14159 ≈ 904.78 cm³ Step 4: Verification: For r = 6: 4πr² = 4π(6)² = 144π ✓ (4/3)πr³ = (4/3)π(6)³ = (4/3...

Q5: A hemisphere has radius 8 cm. Find its curved surface area, total surface area (curved + base), and volume.

Step 1: Hemisphere radius: r = 8 cm Step 2: Curved Surface Area (curved part only): Formula: Curved Surface Area = 2πr² Curved Surface Area = 2 × π × 8² Curved Surface Area = 2 × π × 64 Curved Surface Area = 128π cm² Curved Surface Area ≈ 128 × 3.14159 ≈ 402.12 cm² Step 3: Area of Circular Base: Area of base = πr² Area of base = π × 8² Area of base = 64π cm² Area of base ≈ 64 × 3.14159 ≈ 201.06 cm² Step 4: Total Surface Area: Total Surface Area = Curved Surface Area + Base Area Total Surface ...

Q6: A cube has side length 5 cm. Find its total surface area, lateral surface area, and volume.

Step 1: Cube side length: a = 5 cm Step 2: Total Surface Area of Cube: A cube has 6 equal square faces. Formula: Total Surface Area = 6a² Total Surface Area = 6 × 5² Total Surface Area = 6 × 25 Total Surface Area = 150 cm² Step 3: Lateral Surface Area (area of 4 vertical faces): Formula: Lateral Surface Area = 4a² Lateral Surface Area = 4 × 5² Lateral Surface Area = 4 × 25 Lateral Surface Area = 100 cm² Step 4: Verification: Total Surface Area = Lateral Surface Area + 2 × (Base Area) 150 = 10...

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