NCERT Solutions for Class 9 Maths Chapter 12: Heron's Formula

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The NCERT Solutions for Class 9 Maths chapter 12 Heron’s Formula are included in this article. Heron’s Formula is widely used to determine the area of different triangles, such as equilateral, isosceles and scalene triangle. It also helps to determine the area of different polygons, such as a cuboid and cone.

Class 9 Maths Chapter 12 Heron’s Formula belong to Unit 5 Mensuration which has a weightage of 13 marks in the Class 9 Maths Examination. Class 9 Maths Chapter 12 has the following important concepts:

Download: NCERT Solutions for Class 9 Mathematics Chapter 12 pdf

NCERT Solutions for Class 9 Maths Chapter 12

NCERT Solutions

Important Topics in Class 9 Maths Chapter 12 Heron’s Formula

Important Topics in Class 9 Maths Chapter 12 Heron’s Formula are elaborated below:

Volume of a Cuboid

The volume of a Cuboid can be defined as the total space its occupies in three-dimensional space. In geometry, a cuboid has a total of 6 rectangular faces.

Example: Determine the volume of a cuboid which has length 60 cm, breadth 30 cm and height 8 cm.

Solution: As per the given equation,
Length = 90 cm
Breadth = 30 cm
And Height = 15 cm
As we already know the formula, we can say,
Volume of a Cuboid = l × b × h (cubic units)
= (60 × 30 × 8) cm³
= 14,400 cm³

Volume of Right Circular Cone

The volume of a right circular cone can be expressed as its area or capacity of a cone.

Example: Determine the volume of a conical figure that has a radius of 9 feet and a height of 14 feet.

Solution: As per the given equation,
r = 9 feet
h = 14 feet
The volume of the conical figure is = 1/3 r²h
= ? * 3.14 * (9)² * 14
= 1186.92 cubic feet

Volume of a Sphere

The volume of a sphere refers to the total amount of space it occupies. The volume of a sphere is measured in cubic units, like m³, cm³, in³and more.

Example: Determine the volume of a sphere that has a radius of 5 cm.

Solution: As we already know the volume of a sphere, we can say,
V = 4/3 πr³
= (4/3) x 3.14 x 5³
= (4/3) x 3.14 x 5 x 5 x 5
= 523.3 cm³

NCERT Solutions for Class 9 Maths Chapter 12 Exercises:

The detailed solutions for all the NCERT Solutions for Heron’s Formula under different exercises are:

Also check:

Unit Related Topics
Heron's Formula	Difference between Area and Volume	Equilateral Triangle
Formula Of Perimeter Shapes	Line segment	Properties of Triangle
Types Of Triangles	Scalene Triangle	Area of a Kite Formula

Also Read:

Math Study Guides
Maths Important Formulas	Maths MCQs	Comparison Articles in Maths
Difference Between Topics in Maths	Math Study Material	Algebra
Trigonometry	Number Systems	Mensuration
Math Formula	NCERT Solutions for Class 9 Maths	Geometry

CBSE X Related Questions

1.
In the figure given above, $\triangle ABC \sim \triangle XYZ$, then find the values of $x$ and $y$.
View Solution
2.
Assertion (A) : H.C.F. $(36 m^{2}, 18 m) = 18 m$, where $m$ is a prime number.
Reason (R) : H.C.F. of two numbers is always less than or equal to the smaller number.
- Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).
- Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).
- Assertion (A) is true, but Reason (R) is false.
- Assertion (A) is false, but Reason (R) is true.
View Solution
3.
The first term of an AP is $p$ and the common difference is $q$, then its 10th term is :
- $q - 9p$
- $p - 9q$
- $p + 9q$
- $2p + 9q$
View Solution
4.
If the pair of linear equations : $ a_1x + b_1y + c_1 = 0 $ and $ a_2x + b_2y + c_2 = 0 $ is consistent and dependent, then
- $ \frac{a_1}{a_2} \neq \frac{b_1}{b_2} $
- $ \frac{a_1}{a_2} = \frac{b_1}{b_2} = \frac{c_1}{c_2} $
- $ \frac{a_1}{a_2} = \frac{b_1}{b_2} \neq \frac{c_1}{c_2} $
- $ \frac{a_1}{a_2} = \frac{b_1}{b_2} = \frac{c_1}{c_2} $
View Solution
5.
A kite is flying at a height of $60 \text{ m}$ above the ground level. Ravi, standing at the roof of the house is holding the string straight and observes the angle of elevation of kite as $30^{\circ}$. From the bottom of the same building, the angle of elevation of kite is $45^{\circ}$. Find the length of the string and height of roof from the ground. (Use $\sqrt{3} = 1.73$)
View Solution
6.
Two water taps together can fill a tank in $8\frac{8}{9}$ hours. The tap of larger diameter takes 4 hours less than the smaller one to fill the tank separately. Find the time in which each tap can separately fill the tank.
View Solution

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NCERT Solutions for Class 9 Maths Chapter 12: Heron's Formula