Mensuration

Important Questions

In ICSE Class 10 Mathematics, Chapter 17 focuses on “Mensuration.” This chapter deals with the measurement of geometric figures, such as areas and volumes. It is an essential part of mathematics as it helps students understand and calculate the sizes and capacities of various shapes and objects.

Table of Contents

In Class 10 ICSE (Indian Certificate of Secondary Education) mathematics, the chapter on “Mensuration” is a fundamental topic that deals with the measurement of geometric figures, including calculating their areas and volumes. Mensuration is a practical and essential part of mathematics with numerous real-world applications. Mensuration is not just a mathematical concept; ICSE class 10 maths mensuration is a practical tool that helps us quantify and measure objects in our everyday lives. Whether you’re designing a building, calculating the area of a land plot, or estimating the volume of a container, mensuration plays a vital role in solving real-world problems accurately. Here are some area and volume class 10 ICSE questions.

Mensuration is the branch of mathematics that focuses on measuring the sizes, areas, and volumes of various geometric shapes and figures. ICSE class 10 maths mensuration provides us with the tools and formulas to quantify and understand the spatial properties of objects in both two and three dimensions.

**Key Concepts and Objectives:**

**Area and Perimeter:** Mensuration helps us calculate the area (space inside a shape) and perimeter (the boundary length) of 2D figures such as rectangles, squares, circles, and triangles.

**Volume:** It allows us to determine the volume (space occupied) of 3D figures like cubes, cuboids, cylinders, cones, and spheres.

**Formulas:** Mensuration provides us with specific formulas and methods for each type of shape, making it possible to compute measurements accurately.

**Ans.** (C) 660 cm^3 \\
**Explanation:**

volume of cone = (1/3) πr^2h = 220 cm^3 \\
\text{Volume of cylinder} = πr^2h = 3×220 cm^3 \\
(∵ radius and height of cylinder are as same as that of cone)

(b) area of the cricle > area of the square

(c) area of the circle < area of the square

(d) none of these

**Ans.** (b)

**Explanation:**

Circumference of circle = 2πR Perimeter of square = 4a

According to question 2πR = 4a

⇒ πR = 2a

⇒ \frac{\pi R}{2} = a \\
\text{Area of square =} a^2 \\
= \left(\frac{\pi R}{2}\right )^2 \\
=\frac{\pi^2 R^2}{4} \\
\begin{bmatrix} \because \pi = 3.14 \space \space and \space \space 3.14 \lt 4 \\
\therefore \frac{3.14}{4}\lt 1\end{bmatrix} \\
π R^2> \frac{\pi}{4} π R^2 \\
Area of circle > Area of square

(ii) How much steel was actually used, if \space \frac{1}{2} \space of the steel actually used was wasted in making the closed tank.

**Explanation:**

(i) Here,

r= \frac{4.0}{2} = 2m \space and \space h = 4⋅4 m \\
\text{Curved surface area =} 2πrh m^2 \\
=2× \frac{22}{7} ×2×4⋅4 cm^2 \\
= 55.31 m^2 \\
(ii) Since \frac{1}{2} of the actual steel used was wasted, the area of the steel which has gone into the tank = \begin{pmatrix}1- \frac{1}{12}\end{pmatrix} = \frac{11}{12} of x, where

x = total area of steel used . Steel used = (2πrh + 2πr^2) m^2 \\
=(55⋅31+2× \frac{22}{7} ×4) m^2 \\
= (55·31 + 25·14) m^2 \\
= 80·45 m^2 \\
∴ \frac{11}{12}x =80.45 \\
⇒ x = 87·76 m^2 \\
Hence, the actual area of the steel used = 87·76 m^2.

**Explanation:**

Cylindrical area=2πrh

= 2 × \frac{22}{7} × \frac{105}{2} ×3 m^2 \\
= and conical area = πrl

=\frac{22}{7} × \frac{105}{2} × 53 m^2

=1947 m.

**Explanation:**

Height of the tent = Height of cone + Height of the cylinder

H = height of cone = 20 m

∴ Height of cylinder

= h = 60 – 20 = 40 m

and Radius of cone = Radius of cylinder r = 10 m

∴ Volume of the tent = Volume of cylinder+ Volume of the cone=πr^2h + \frac{1}{3} πr^2H \\
= πr^2 \begin{pmatrix}h+ \frac{H}{3}\end{pmatrix} \\
= π(10)^2 \begin{pmatrix} 40+ \frac{20}{3}\end{pmatrix} \\
=100 × \frac{22}{7} \begin{pmatrix}\frac{140}{3}\end{pmatrix} \\
= 14666·6 m^3 \\
Slant height of the cone is I= \sqrt{H^2+r^2} \\
= \sqrt{400+100} \\
= \sqrt{500} = \sqrt[10]{5} m
Since, curved surface area of cone= πrl

= \frac{22}{7} ×10×10 \sqrt{5} m^2
and curved surface area of cylinder

= 2πrh=2× \frac{22}{7} ×10×40
∴ Total surface area of the canvas in making the tent

= C.S.A. of cylinder + C.S.A. of cone

= 2πrh + πrl

= πr (2h + l)

= \frac{22}{7} ×10(2×40+10 \sqrt{5})m^2\\
= \frac{220}{7} (80+10 \sqrt{5})m^2\\
\text{Total Surface Area =} 3217·04 m^2

Chapter No. | Chapter Name |
---|---|

Chapter 1 | Goods and Service Tax (GST) |

Chapter 2 | Banking |

Chapter 3 | Shares and Dividends |

Chapter 4 | Linear inequations |

Chapter 5 | Quadratic Equations in one variable |

Chapter 6 | Ratio and proportion |

Chapter 7 | Factorization |

Chapter 8 | Matrices |

Chapter 9 | Arithmetic Progression |

Chapter 10 | Geometric Progression |

Chapter 11 | Coordinate Geometry |

Chapter 12 | Reflection |

Chapter 13 | Similarity |

Chapter 14 | Loci |

Chapter 15 | Circles |

Chapter 16 | Constructions |

Chapter 17 | Mensuration |

Chapter 18 | Trigonometry |

Chapter 19 | Statistics |

Chapter 20 | Probability |

In conclusion, the chapter on ICSE class 10 maths mensuration is an integral part of the curriculum, offering students the essential knowledge and skills to measure and calculate areas and volumes of geometric shapes. These concepts extend far beyond the classroom, finding application in various real-world scenarios such as construction, design, and everyday problem-solving. Mastery of mensuration equips students with a valuable toolkit for understanding and quantifying the spatial attributes of objects, laying the foundation for more advanced mathematical concepts and practical life applications.
If you want to get better at this chapter and really understand it, check out oswal.io. They have lots of extra questions to help you practice and get a deeper grasp of the ideas. It’s like having a treasure chest of knowledge to make you a math wizard!

Ans: Mensuration in mathematics is the study of measuring and calculating the areas and volumes of geometric shapes and figures.

Ans: Mensuration is crucial because it helps us quantify and understand the sizes of objects in real-world situations, including construction, design, and everyday problem-solving.

Ans: Common 2D shapes include rectangles, squares, circles, triangles, and parallelograms.

Ans: The area of a rectangle is calculated by multiplying its length and width (A = length × width).

Ans: The perimeter of a square is four times the length of one of its sides (P = 4 × side length).

Chapter Wise Important Questions for ICSE Board Class 10 Mathematics |
---|

Goods and Service Tax (GST) |

Banking |

Shares and Dividends |

Linear inequations |

Quadratic Equations in one variable |

Ratio and proportion |

Factorization |

Matrices |

Arithmetic Progression |

Geometric Progression |

Coordinate Geometry |

Reflection |

Similarity |

Loci |

Circles |

Constructions |

Mensuration |

Trigonometry |

Statistics |

Probability |

CBSE Important Questions Class 9

CBSE Important Questions Class 10

CBSE Important Questions Class 12

- CBSE Class 12 English
- CBSE Class 12 Maths
- CBSE Class 12 Physics
- CBSE Class 12 Biology
- CBSE Class 12 Chemistry
- CBSE Class 12 Computer Science
- CBSE Class 12 Business Study
- CBSE Class 12 Economics
- CBSE Class 12 Physical Education

CBSE Practice Papers

CBSE Practice Papers

ICSE Important Questions Class 9

- ICSE Class 9 Maths
- ICSE Class 9 Physics
- ICSE Class 9 Chemistry
- ICSE Class 9 Biolog1y
- ICSE Class 9 History & Civics
- ICSE Class 9 Geography
- ICSE Class 9 Computer Applications

ICSE Important Questions Class 10

ICSE Practice Papers

- ICSE Class 10 Physics
- ICSE Class 10 Chemistry
- ICSE Class 10 Biology
- ICSE Class 10 Maths

ISC Important Questions Class 12

- ISC Class 12 Physics
- ISC Class 12 Chemistry
- ISC Class 12 Biology
- ISC Class 12 Maths
- ISC Class 12 Economics
- ISC Class 12 Physical Education
- ISC Class 12 Computer Science

ISC Practice Papers

- ISC Class 12 Physics
- ISC Class 12 Chemistry
- ISC Class 12 Biology
- ISC Class 12 Maths

Contact Us

Noida - 201309, Uttar Pradesh

© Copyright 2024 **oswal.io** by **OSWAL PUBLISHERS** Simplifying Exams