23. Complete Mensuration Revision & Practice

Welcome to the Complete Mensuration Revision section.

This part brings together the important formulas covered in the Mensuration series and provides practice questions for competitive examinations.

Note: This revision section is an extension for your website. It is not a separate topic/page in the original PDF. The original PDF ends with Hemisphere, Prism and Pyramid.

1. Basic Mensuration Formulas

Perimeter = Sum of all sides

Area = Surface covered by a plane figure

Volume = Space occupied by a solid

Remember:

Perimeter → linear units
Area → square units
Volume → cubic units

2. Important 2D Figure Formulas

Figure	Important Formula
Square	Area = a²
Rectangle	Area = L × B
Triangle	Area = ½ × Base × Height
Parallelogram	Area = Base × Height
Rhombus	Area = ½ × d₁ × d₂
Trapezium	Area = ½ × (a+b) × h
Circle	Area = πr²
Circle	Circumference = 2πr

3. Circle Revision

Diameter = 2r

Radius = Diameter ÷ 2

Area = πr²

Circumference = 2πr

Area of Semicircle = ½πr²

4. Important 3D Solid Formulas

Solid	Volume	Surface Area
Cube	a³	TSA = 6a²
Cuboid	LBH	TSA = 2(LB+BH+HL)
Cylinder	πr²h	TSA = 2πr(r+h)
Cone	⅓πr²h	TSA = πr(r+l)
Sphere	⁴⁄₃πr³	4πr²
Hemisphere	²⁄₃πr³	3πr²

5. Hemisphere Quick Revision

Volume = ²⁄₃πr³

CSA = 2πr²

TSA = 3πr²

The original PDF specifically gives these three formulas for the hemisphere. :contentReference[oaicite:1]{index=1}

6. Prism & Pyramid Quick Revision

Prism

Volume = Base Area × Height

LSA = Base Perimeter × Height

TSA = LSA + 2 × Base Area

Pyramid

Volume = ⅓ × Base Area × Height

LSA = ½ × Base Perimeter × Slant Height

TSA = LSA + Base Area

These formulas are shown on the final page of the original PDF. :contentReference[oaicite:2]{index=2}

7. Solved Example

Example: Cylinder

A cylinder has radius 7 cm and height 10 cm. Find its volume. Take π = 22/7.

V = πr²h

= ²²⁄₇ × 7² × 10

= 22 × 7 × 10

V = 1540 cm³

8. Mensuration Practice Questions

1. Find the area of a square whose side is 12 cm.

2. Find the area of a rectangle whose length is 15 cm and breadth is 8 cm.

3. Find the area of a triangle whose base is 20 cm and height is 12 cm.

4. Find the circumference of a circle whose radius is 7 cm. Take π = 22/7.

5. Find the area of a circle whose radius is 14 cm. Take π = 22/7.

6. Find the volume of a cube whose edge is 8 cm.

7. Find the volume of a cuboid with L = 10 cm, B = 6 cm and H = 5 cm.

8. Find the volume of a cylinder with radius 7 cm and height 8 cm. Take π = 22/7.

9. Find the volume of a cone with radius 7 cm and height 12 cm. Take π = 22/7.

10. Find the surface area of a sphere whose radius is 7 cm. Take π = 22/7.

11. Find the volume of a hemisphere whose radius is 7 cm. Take π = 22/7.

12. Find the TSA of a hemisphere whose radius is 7 cm. Take π = 22/7.

13. A prism has base area 40 cm² and height 10 cm. Find its volume.

14. A pyramid has base area 60 cm² and height 9 cm. Find its volume.

9. Answers

Question	Answer
1	144 cm²
2	120 cm²
3	120 cm²
4	44 cm
5	616 cm²
6	512 cm³
7	300 cm³
8	1232 cm³
9	616 cm³
10	616 cm²
11	718.67 cm³ approximately
12	462 cm²
13	400 cm³
14	180 cm³

10. Important Exam Tips

Tip 1: Identify the figure before selecting the formula.

Tip 2: Check whether the question asks for area, perimeter, surface area or volume.

Tip 3: If diameter is given, convert it to radius before using circle formulas.

r = d ÷ 2

Tip 4: Area is expressed in square units.

Tip 5: Volume is expressed in cubic units.

Tip 6: In 3D questions, carefully distinguish between CSA, LSA and TSA.

Tip 7: In cone and pyramid questions, do not confuse vertical height with slant height.

11. Final One-Minute Formula Revision

Square Area = a²

Rectangle Area = L × B

Triangle Area = ½ × b × h

Circle Area = πr²

Circle Circumference = 2πr

Cube Volume = a³

Cuboid Volume = LBH

Cylinder Volume = πr²h

Cone Volume = ⅓πr²h

Sphere Volume = ⁴⁄₃πr³

Hemisphere Volume = ²⁄₃πr³

Prism Volume = Base Area × Height

Pyramid Volume = ⅓ × Base Area × Height

Source Note: The original uploaded Mensuration PDF contains 11 pages and ends with the Surface Area & Volume section covering Sphere, Hollow Sphere, Hemisphere, Prism and Pyramid. :contentReference[oaicite:3]{index=3}

This Part 23 is therefore a revision and practice extension, rather than a new formula page from the PDF.