Important Questions on Mensuration for Class 8

Important Questions on Mensuration for Class 8 are available in this Maths article. Important Questions on Mensuration for Class 8 are very useful to solve the problems easily. This article helps the students to know the key questions and answers about Mensuration. Mensuration measures area, perimeter and volume of shapes which we use in our day to day calculations.

Our subject experts have provided detailed solutions for these problems based on the CBSE syllabus and the NCERT textbook. This material helps students revise the chapter easily and perform well in the final examination.

Table of Contents

• Exercise 11.1: Introduction to Mensuration and Basic Concepts
• Exercise 11.2: Area of Trapezium
• Exercise 11.3: Area of Polygon
• Exercise 11.4: Introduction to Solid Shapes
• Exercise 11.5: Surface Area of Cube, Cuboid, and Cylinder
• Exercise 11.6: Volume of Cube, Cuboid, and Cylinder
• Tips for Solving Mensuration Problems

Exercise 11.1: Introduction to Mensuration and Basic Concepts

This exercise focuses on understanding fundamental mensuration concepts, understanding area and perimeter, and recalling basic formulas for common shapes.

Question 1: Define Mensuration

Answer: Mensuration is the branch of mathematics that deals with the measurement of lengths, areas, volumes, and other geometric properties of figures. It involves using formulas and calculations to find measurements like perimeter, area, and volume of different shapes, both two-dimensional and three dimensional.

Question 2: What is the Difference Between Perimeter and Area?

Answer: Perimeter refers to the total distance around a shape, measured along its boundary. It is measured in linear units (like cm, m, km).

Area, on the other hand, refers to the total space covered by a shape. It is measured in square units (like cm², m², km²).

Example: For a rectangle with length 5 cm and width 3 cm:

• Perimeter = 2(length + width) = 2(5 + 3) = 16 cm
• Area = length × width = 5 × 3 = 15 cm²

Question 3: Find the Perimeter of a Rectangle with Length 8 cm and Width 5 cm

Solution: Perimeter of rectangle = 2(length + width) = 2(8 + 5) = 2(13) = 26 cm

Answer: 26 cm

Question 4: Calculate the Area of a Square with Side 7 cm

Solution: Area of square = side × side = side² = 7 × 7 = 49 cm²

Answer: 49 cm²

Question 5: Find the Perimeter and Area of a Triangle with Sides 5 cm, 6 cm, and 7 cm

Solution: Perimeter = sum of all sides = 5 + 6 + 7 = 18 cm

For area, we use Heron's formula: Semi-perimeter (s) = (5 + 6 + 7)/2 = 18/2 = 9 cm

Area = √[s(s-a)(s-b)(s-c)]

= √[9(9-5)(9-6)(9-7)]

= √[9 × 4 × 3 × 2]

= √[216]

= 14.7 cm² (approximately)

Answer: Perimeter = 18 cm, Area ≈ 14.7 cm²

Question 6: Find the Area of a Circle with Radius 7 cm

Solution: Area of circle = πr² = (22/7) × 7 × 7 = (22/7) × 49 = 22 × 7 = 154 cm²

Answer: 154 cm²

Exercise 11.2: Area of Trapezium

This exercise focuses on understanding trapeziums and calculating their areas using the trapezium area formula.

Question 7: Define a Trapezium

Answer: A trapezium is a quadrilateral with one pair of parallel sides. The parallel sides are called bases, and the non-parallel sides are called legs. A trapezium has four vertices, four angles, and four sides.

• Only one pair of opposite sides is parallel
• The sum of angles is 360°
• It can be isosceles (equal legs) or scalene

Question 8: What is the Formula for the Area of a Trapezium?

Answer: The area of a trapezium is given by the formula:

Area = (1/2) × (sum of parallel sides) × height

Or: Area = (1/2) × (a + b) × h

Where:

• a and b are the lengths of the two parallel sides (bases)
• h is the perpendicular distance between the parallel sides (height)

Question 9: Find the Area of a Trapezium with Parallel Sides 10 cm and 8 cm, and Height 5 cm

Solution: Area = (1/2) × (sum of parallel sides) × height = (1/2) × (10 + 8) × 5 = (1/2) × 18 × 5 = (1/2) × 90 = 45 cm²

Answer: 45 cm²

Question 10: A Trapezium has Parallel Sides of 12 cm and 6 cm. If its Area is 90 cm², Find the Height

Solution: Area = (1/2) × (a + b) × h 90 = (1/2) × (12 + 6) × h 90 = (1/2) × 18 × h 90 = 9h h = 90/9 = 10 cm

Answer: Height = 10 cm

Question 11: Calculate the Area of a Trapezium with Bases 15 cm and 20 cm, and Height 8 cm

Solution: Area = (1/2) × (a + b) × h = (1/2) × (15 + 20) × 8 = (1/2) × 35 × 8 = (1/2) × 280 = 140 cm²

Answer: 140 cm²

Question 12: A Trapezium has Area 60 cm² and one Parallel Side 8 cm. If the Height is 6 cm, Find the Other Parallel Side

Solution: Area = (1/2) × (a + b) × h 60 = (1/2) × (8 + b) × 6 60 = 3 × (8 + b) 60 = 24 + 3b 36 = 3b b = 12 cm

Answer: Other parallel side = 12 cm

Exercise 11.3: Area of Polygon

This exercise covers calculating areas of various polygons including quadrilaterals and compound shapes.

Question 13: Find the Area of a Quadrilateral with Diagonals 10 cm and 8 cm that are Perpendicular

Solution: For a quadrilateral with perpendicular diagonals, the area formula is:

Area = (1/2) × d₁ × d₂

Where d₁ and d₂ are the diagonals.

Area = (1/2) × 10 × 8 = (1/2) × 80 = 40 cm²

Answer: 40 cm²

Question 14: Calculate the Area of a Rhombus with Diagonals 12 cm and 8 cm

Solution: Area of rhombus = (1/2) × d₁ × d₂ = (1/2) × 12 × 8 = (1/2) × 96 = 48 cm²

Answer: 48 cm²

Question 15: Find the Area of a Parallelogram with Base 15 cm and Height 10 cm

Solution: Area of parallelogram = base × height = 15 × 10 = 150 cm²

Answer: 150 cm²

Question 16: A Parallelogram has Area 120 cm² and Base 12 cm. Find its Height

Solution: Area = base × height 120 = 12 × h h = 120/12 = 10 cm

Answer: Height = 10 cm

Question 17: Calculate the Area of a Triangle with Base 20 cm and Height 12 cm

Solution: Area of triangle = (1/2) × base × height = (1/2) × 20 × 12 = (1/2) × 240 = 120 cm²

Answer: 120 cm²

Exercise 11.4: Introduction to Solid Shapes

This exercise introduces three-dimensional shapes and helps students understand surface area and volume concepts for solids.

Question 18: What is the Difference Between Surface Area and Volume?

Answer: Surface Area is the total area of all the outer surfaces of a solid shape. It is measured in square units (cm², m², etc.).

Volume is the amount of space occupied by a solid shape. It is measured in cubic units (cm³, m³, etc.).

Example: For a cube with side 5 cm:

• Surface Area = 6 × 5² = 150 cm²
• Volume = 5³ = 125 cm³

Question 19: Define Cube and Cuboid

Answer: A Cube is a three-dimensional solid with:

• 6 square faces
• 12 equal edges
• 8 vertices
• All dimensions (length, width, height) are equal

A Cuboid (or Rectangular Prism) is a three-dimensional solid with:

• 6 rectangular faces
• 12 edges
• 8 vertices
• Three different dimensions (length, width, height)

Question 20: What is a Cylinder?

Answer: A cylinder is a three-dimensional solid shape with:

• 2 circular bases (top and bottom) that are parallel and equal
• 1 curved lateral surface
• A height (distance between the two bases)
• A radius (distance from center to edge of circular base)

The cylinder has no edges or vertices where curved and flat surfaces meet, though it has circular edges where the bases meet the lateral surface.

Question 21: List the Formulas for Surface Area and Volume of a Cube with Side 'a'

Answer: For a cube with side 'a':

Surface Area = 6a² (since a cube has 6 square faces, each with area a²)

Volume = a³ (length × width × height = a × a × a)

Question 22: Write the Formulas for Surface Area and Volume of a Cuboid with Dimensions l, w, h

Answer: For a cuboid with length 'l', width 'w', and height 'h':

Surface Area = 2(lw + wh + lh) (sum of areas of all 6 faces)

Volume = l × w × h (length × width × height)

Exercise 11.5: Surface Area of Cube, Cuboid, and Cylinder

This exercise develops proficiency in calculating surface areas of three-dimensional solid shapes.

Question 23: Find the Surface Area of a Cube with Side 5 cm

Solution: Surface Area of cube = 6a² = 6 × 5² = 6 × 25 = 150 cm²

Answer: 150 cm²

Question 24: Calculate the Surface Area of a Cuboid with Length 10 cm, Width 8 cm, and Height 6 cm

Solution: Surface Area = 2(lw + wh + lh) = 2(10×8 + 8×6 + 10×6) = 2(80 + 48 + 60) = 2(188) = 376 cm²

Answer: 376 cm²

Question 25: Find the Surface Area of a Cylinder with Radius 7 cm and Height 10 cm

Solution: Surface Area of cylinder = 2πr(h + r) Or = 2πrh + 2πr² (curved surface area + area of two bases)

Using 2πr(h + r): = 2 × (22/7) × 7 × (10 + 7) = 2 × (22/7) × 7 × 17 = 2 × 22 × 17 = 44 × 17 = 748 cm²

Answer: 748 cm²

Question 26: Calculate the Curved Surface Area of a Cylinder with Radius 5 cm and Height 12 cm

Solution: Curved Surface Area (Lateral Surface Area) = 2πrh = 2 × (22/7) × 5 × 12 = 2 × (22/7) × 60 = (2 × 22 × 60)/7 = 2640/7 = 377.14 cm² (approximately)

Answer: 377.14 cm² (or 2640/7 cm²)

Question 27: A Cube has Surface Area 294 cm². Find the Length of its Side

Solution: Surface Area = 6a² 294 = 6a² a² = 294/6 = 49 a = 7 cm

Answer: Side length = 7 cm

Question 28: Find the Total Surface Area of a Cylinder with Radius 4 cm and Height 8 cm

Solution: Total Surface Area = 2πr(h + r) = 2 × (22/7) × 4 × (8 + 4) = 2 × (22/7) × 4 × 12 = 2 × (22/7) × 48 = (2 × 22 × 48)/7 = 2112/7 = 301.71 cm² (approximately)

Answer: 301.71 cm² (or 2112/7 cm²)

Exercise 11.6: Volume of Cube, Cuboid, and Cylinder

This exercise focuses on calculating volumes of three-dimensional solid shapes.

Question 29: Find the Volume of a Cube with Side 6 cm

Solution: Volume of cube = a³ = 6³ = 216 cm³

Answer: 216 cm³

Question 30: Calculate the Volume of a Cuboid with Dimensions 12 cm, 10 cm, and 8 cm

Solution: Volume = l × w × h = 12 × 10 × 8 = 960 cm³

Answer: 960 cm³

Question 31: Find the Volume of a Cylinder with Radius 7 cm and Height 10 cm

Solution: Volume of cylinder = πr²h = (22/7) × 7² × 10 = (22/7) × 49 × 10 = 22 × 7 × 10 = 1540 cm³

Answer: 1540 cm³

Question 32: A Cuboid has Volume 240 cm³. If Length is 8 cm and Width is 6 cm, Find the Height

Solution: Volume = l × w × h 240 = 8 × 6 × h 240 = 48h h = 240/48 = 5 cm

Answer: Height = 5 cm

Question 33: Calculate the Volume of a Cylinder with Radius 5 cm and Height 14 cm

Solution: Volume = πr²h = (22/7) × 5² × 14 = (22/7) × 25 × 14 = (22 × 25 × 14)/7 = (22 × 25 × 2) = 1100 cm³

Answer: 1100 cm³

Question 34: A Cube has Volume 343 cm³. Find the Length of its Side

Solution: Volume = a³ 343 = a³ a = ∛343 = 7 cm

Answer: Side length = 7 cm

Question 35: A Cylinder has Volume 770 cm³ and Height 10 cm. Find its Radius

Solution: Volume = πr²h 770 = (22/7) × r² × 10 770 = (220/7) × r² r² = (770 × 7)/220 r² = 5390/220 r² = 24.5 r ≈ 4.95 cm (approximately 5 cm)

Answer: Radius ≈ 5 cm

Mixed Exercise Questions

This section contains challenging questions that combine concepts from multiple exercises.

Question 36: A Rectangular Field has Length 40 m and Width 30 m. It is Surrounded by a Path of Width 2 m. Find the Area of the Path

Solution: Outer dimensions: (40 + 2×2) × (30 + 2×2) = 44 × 34 Area of outer rectangle = 44 × 34 = 1496 m²

Area of inner rectangle = 40 × 30 = 1200 m²

Area of path = Area of outer rectangle - Area of inner rectangle = 1496 - 1200 = 296 m²

Answer: 296 m²

Question 37: A Cube and a Cuboid have the Same Volume. The Cube has Side 6 cm, and the Cuboid has Dimensions 8 cm × 6 cm × ?. Find the Missing Dimension

Solution: Volume of cube = 6³ = 216 cm³

Volume of cuboid = l × w × h 216 = 8 × 6 × h 216 = 48h h = 216/48 = 4.5 cm

Answer: Missing dimension = 4.5 cm

Question 38: A Room is 10 m Long, 8 m Wide, and 4 m High. Find the Cost of Painting its Walls at Rs. 50 per m² (Floor and Ceiling are Not Painted)

Solution: Area of four walls = 2(length × height + width × height) = 2(10 × 4 + 8 × 4) = 2(40 + 32) = 2(72) = 144 m²

Cost = 144 × 50 = Rs. 7200

Answer: Rs. 7200

Question 39: A Cylindrical Tank has Radius 2 m and Height 7 m. Find the Cost of Painting its Outer Surface at Rs. 40 per m² (Top and Bottom are Not Painted)

Solution: Curved Surface Area = 2πrh = 2 × (22/7) × 2 × 7 = 2 × 22 × 2 = 88 m²

Cost = 88 × 40 = Rs. 3520

Answer: Rs. 3520

Question 40: A Swimming Pool is 20 m Long, 15 m Wide, and 2 m Deep. How Many Liters of Water Can it Hold?

Solution: Volume = l × w × h = 20 × 15 × 2 = 600 m³

1 m³ = 1000 liters

Volume in liters = 600 × 1000 = 600,000 liters

Answer: 600,000 liters

Tips for Solving Mensuration Problems

1. Draw the shape to see it clearly and spot all sizes.
2. Note all measurements like length, width, height, or radius.
3. Pick the right formula for that shape.
4. Make sure units match; change them if needed.
5. Do calculations step by step using BODMAS order.
6. Use 22/7 or 3.14 for π as the problem says.
7. Check if the answer makes sense for the size.
8. Always add units like cm, cm², or cm³.