Surface Area Volume in 5 Minutes — Free Quick Revision
Learn Surface Area Volume in about 5 minutes — a free bite-sized module with a clear explanation, a worked example and a quick quiz for Indian students.
TL;DR: Learn Surface Area Volume in about 5 minutes — a free bite-sized module with a clear explanation, a worked example and a quick quiz for Indian student…
Written & reviewed by the Syllab.in Academic Team (CBSE/NCERT subject experts) · Updated
Surface area is the total area of all faces. Volume is the space inside. Know the formulas for sphere, cone, and cylinder.
Maths · Class 10 · about 8 minutes
The Idea
Surface Area is the total area of all outer faces of a 3D shape. Volume is the amount of space inside the shape.
Cylinder (radius r, height h): - Surface area = 2πr² + 2πrh (two circular bases + curved side) - Volume = πr²h
Cone (radius r, height h, slant height l): - Surface area = πr² + πrl (base + curved surface) - Volume = (1/3)πr²h
Sphere (radius r): - Surface area = 4πr² - Volume = (4/3)πr³
These formulas appear frequently in competitive exams and real-world problems (water tanks, ice cream cones, planets).
Tip: Volume is always in cubic units (cm³, m³), and surface area in square units (cm², m²).
Worked Example: Volume of a Cone
Problem. A cone has radius 5 cm and height 12 cm. Find its volume.
Solution.
Volume = (1/3)πr²h Volume = (1/3)π(5)²(12) Volume = (1/3)π(25)(12) Volume = (1/3)π(300) Volume = 100π cm³ Volume ≈ 314.16 cm³
Quick Quiz
Answer each one before reading the explanation beneath it.
1. A sphere has radius 3 cm. What is its surface area?
- 36π cm² — correct
- 9π cm²
- 12π cm²
- 81π cm²
36π cm²
2. A cylinder has radius 2 cm and height 10 cm. What is its volume?
- 40π cm³ — correct
- 20π cm³
- 80π cm³
- 60π cm³
40π cm³
3. Which shape has the smallest surface area for the same volume?
- Cube
- Cylinder
- Sphere — correct
- Cone
Sphere
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