Case Study Based -3
The art department of a school prepared circular hanging of the
annual function of the school. The circle with diameter 42 cm was
placed at the bottom and the size of the middle circle was half the
size of the bottom one and the smallest circle was half the size of the
middle circle.
Answers
Given : The art department of a school prepared circular hanging for the annual function of the school.
The circle with diameter 42 cm was placed at the bottom and the size of the middle circle was half the size of the bottom one and the smallest circle was half the size of the middle circle.
To Find : (i)the radius of the small circle is?
(ii)the area of middle circle is?
(iii) the area of bottom circle region that is visible is?
(iv) the ratio of areas of three circles, starting from the bottom circle is?
(v) a colorful tape was used to decorate the boundary of the bottom circle. the length of tape used is
Solution:
Bottom circle Diameter = 42 cm
=> Radius = 42/2 = 21 cm
Size = Area = πr² = (22/7) (21)² = 1386 cm²
Area of middle circle = (1/2) 1386 = 693 cm²
Area of small circle = 693/2
(22/7)r² = 693/2
=>r² = 441/4
=> r = 21/2 cm
the area of bottom circle region that is visible is = area of larger - area of middle
= 1386 - 693
= 693 cm²
the ratio of areas of three circles, starting from the bottom circle is
1386 : 693 : 693/2
2 : 1 : 1/2
4 : 2 : 1
a colorful tape was used to decorate the boundary of the bottom circle. the length of tape used is = 2πr
= 2 * 22/7 * 21
= 44 * 3
= 132 cm
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