Class 10 case study Chapter 11 Area related to circle 2

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Class 10 Chapter 11(Area related to circle)

The south central zone of Indian Railways has commissioned the longest electrified railway tunnel in the country. According to local media reports, the construction of the 6.6 km long tunnel took 43 months to complete. The electrified railway tunnel is situated between Chelopalli and Rapuru station as a part of the Obulavaripalli-venkatachalam railway line. The tunnel is expected to facilitate freight movement in the region,reducing the distance between Krishnapatnam port and Hinterland areas by nearly 60 km.(Class 10 case study Chapter 11 Area related to circle)

The adjoining figure shows a cross section of the railway tunnel, which is a part of a circle. The radius OA of the circular part is 4 m and ∠AOB = 90°.

(A) Considering the tunnel to the part of a circle as shown below, find the area of minor segment is.

(B) Find the perimeter of the cross section .

Solution:

(A) Area of minor segment = Area of sector AOB – Area of ΔOAB

= \dfrac{\theta}{360}\times \pi r^2 - \dfrac{1}{2}\times OA \times OB

= \dfrac{90}{360}\times \pi (4)^2 - \dfrac{1}{2}\times 4 \times 4

= 4 \pi - 8

= 4(\pi - 2) m^2

(B) Radius of ΔAOB   = 4 m

∠AOB = 90°

Angle of majoe sector = 270

Using pythagoras theorem

AB^2 = OA^2 + OB^2

\Rightarrow AB^2 = (4)^2 + (4)^2

\Rightarrow AB^2 = 16 + 16 = 32

⇒ AB = 4√2 m

Arc length of major sector AB = \dfrac{\theta}{360}\times 2 \pi r

= \dfrac{270}{360} \times 2 \pi \times 4

=  6 π

Perimeter of cross section = Arc length of major sector + Chord AB

= 6 π + 4√2

= 2(3π + 2√2) m


Question

We all love to eat pizzas, especially kids. And a variety of pizzas are available in India which have been modified according to Indian taste and menu. From the Greeks to the Egyptians, from the persians to the Indians, there have been incarnations of pizza served throughout history. Flatebreads, naan and plakountos are all early preparations that could be considered cousins to the modern pizza, but there is not a consensus as to which is first and whether these could even be considered precursors to pizza at all.(Class 10 case study chapter 11 Area related to circle)

Class 10 case study chapter 11 Area related to circle

Consider two pizzas, both of equal diameter, namely, 12 inches. The first pizza marked (i) has been cut into six equal slices, whereas the second pizza marked (ii) has been cut into eight equal slices.

(A) Find the perimeters of each pizza slices shown in (i and ii).

(B) Find the ratio of areas of each slice of pizza (i) and (ii).

Solution: For solution  click here

 

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