Page 27 - CITS - WCS - Mechanical

WORKSHOP CALCULATION - CITS

Q. Find the height of a cylinder whose radius is 7 cm and the total surface area is 968 cm2.

Solution: Let height of the cylinder = h, radius = r = 7cm
Total surface area = 2πr (h + r)
TSA = 2 x (22/7) x 7 x (7+h) = 968
h = 15 cm.
Q. If one side of a square is 4 cm, then what will be its area and perimeter?

Solution: Given,
Length of side of square = 4 cm
Area = side2 = 4 = 4 x 4 = 16 cm 2
2
Perimeter of square = sum of all its sides
Since, all the sides of the square are equal, therefore;
Perimeter = 4+4+4+4 = 16 cm.
Q. A rectangular piece of dimension 22 cm x 7 cm is used to make a circle of the largest possible radius.
Find the area of the circle formed.
Solution
In questions like this, the diameter of the circle is lesser in length and breadth.
Here, the breadth Diameter of the circle = 7 cm

=> Radius of the circle = 3.5 cm
Therefore, area of the circle = π (Radius)2 = π (3.5) = 38.50 cm .
2
2
Q. A pizza is to be divided into 8 identical pieces. What would be the angle subtended by each piece at
the center of the circle?
Solution:
By identical pieces, we mean that area of each piece is the same.
=> Area of each piece = (π x Radius2 x θ) / 360° = (1/8) x Area of circular pizza

=> (π x Radius2 x θ) / 360° = (1/8) x (π x Radius )
2
=>θ / 360° = 1 / 8
=>θ = 360° / 8 = 45°
Therefore, the angle subtended by each piece at the center of the circle = 45 degree.

1 Find the area of the sector whose angle is 1050, and the perimeter of sector of circle is 18.6 cm.
Given:
Perimeter of a sector of a circle = 18.6 cm
Angle of sector of circle = 105°

To find:
Area = ?
Solution:
θ
Length of Arc (l) = x 2πr unit
360°
105° 22
l = x 2 x x r
360° 7
= 1.83r

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CITS : WCS - Mechanical - Exercise 5