NCERT Solutions for Class 7 Maths Chapter 11 Exercise 11.4

NCERT Solutions for Class 7 Maths Chapter 11 Exercise 11.4 (Ex. 11.4) Perimeter and Area for CBSE and State board students free to use. All the contents are updated for academic session 2020-2021 based on latest NCERT Textbooks.

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Class 7 Maths Chapter 11 Exercise 11.4 Solution

Class: 7Mathematics
Chapter: 11Perimeter and Area
Exercise: 11.4Videos and PDF Solutions

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Circumference and Area of a Circle

Circumference of a Circle

The perimeter of a circle is called its circumference. The length of the thread that winds around the circle exactly gives the circumference of the circle.

An Important Result

The ratio of the circumference of a circle and its diameter is always constant. The result can be verified with the help of the activity given below.
You will find that in each case
circumference / diameter = 3.14 (nearly)
This ratio is denoted by π (called pi)
Thus, π = 3.14 (nearly) = (nearly)
Now, circumference / diameter = π
Or, C /2r = π
Or, C = 2πr
Thus, the circumference of a circle of radius (r) is given by C = 2πr

Note: Unless stated otherwise, we take the value of π as = 3.14

Find the circumference of a circle of radius 10 cm. [ Take π = 3.14]

Here r = 10 cm.
So, circumference= (2πr) units
= (2 x 3.14 x 10) cm = 62.8 cm.
Hence, the circumference of the given circle is 62.8 cm.

The inner circumference of a circular track is 220 m and the width of the track is 7 m. Calculate the cost of putting up a fence along the outer circle of the track at the rate of Rs. 50 per m.

Let the inner and outer radii of the track be r metres and (r + 7) metres respectively.
Inner circumference = 220 m
So, 2πr = 220 m
Or, 2 x 22/7 x r = 220
Because radius of inner track is 35 m
And radius of outer track is (r + 7) = 35 + 7 = 42 m
Circumference of the outer circle = 2 x 22/7 x 42 = 264 m
Rate of fencing = Rs. 50 per meter
So, cost of fencing = Rs. 50 x 264 = Rs 13200



What is the relationship between the circumference and area of a circle?

In geometry, the circumference (from Latin circumferences, meaning “carrying around”) of a circle is the (linear) distance around it. That is, the circumference would be the length of the circle The area of a circle is pi (approximately 3.14) times the radius of the circle squared.

Can the area of a circle ever equal the circumference?

It is possible to have a circle having numerically equal area and circumference. This circle has a radius of 2 units.

The diameter of a wheel of a car is 63 cm. Find the distance travelled by the car during the period in which the wheel makes 1000 revolutions.

Diameter of the wheel = 63 cm
Or, radius of the wheel = cm
Or, circumference of the wheel = 2πr
2 x 22/7 x 63/2 cm = 198 cm = 1.98 m
Distance covered by the wheel in 1 revolution = 1.98 m.
Distance covered by the wheel in 1000 revolutions = (1.98 ´ 1000) m = 1980 m.
Hence, the distance covered by the car = 1980 m

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