Q.1) If the diameter of a circle is increasing by 40% then it's area increases by :
a) 96%
b) 40%
c) 80%
d) 48%
Q.2) The diameters of two circles are 3:4 and sum of the areas of the circles and an equilateral triangle whose diameter and side are respectively equal is :
a) 10 cm , 26 cm
b) 14 cm , 22 cm
c) 18 cm , 24 cm
d) None
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Need a well explained solution.
Answers
Step-by-step explanation:
Q-1:-
Let the diameter of a circle be d units
Area of the circle = πd²/4 sq units -------(1)
40% of d = (40/100)×d
=> (2/5)×d
=> 2d/5 units
If diameter is increased by 40% then
The diameter of the new circle
=> d+(2d/5)
=> (5d+2d)/5
=> 7d/5 units
Area of the new circle
=> π(7d/5)²/4
=> π(49d²/25)/4
=> π(49d²)/(25×4)
=> 49πd²/100 sq.units
Area of the new circle = 49πd²/100 sq.units ----(2)
Increasing in the area
=> New Area - Original area
=> (49πd²/100)-(πd²/4)
=> [(πd²/4)(49/25)]-(πd²/4)
=> (πd²/4)(49/25-1)
=> (πd²/4)[(49-25)/25]
=> (πd²/4)(24/25)
=> (24/25)(πd²/4) sq.units ------------(3)
increased percentage in the area
=> (Increasing in the area/Original area )×100
=> [{(24/25)(πd²/4)}/(πd²/4)]×100
=> (24/25)×100
=> 24×4
=> 96 %
The area is increased by 96%
Q-2:-
Data insufficient.
Answer:
1.(a)
2.(b)
Step-by-step explanation:
Hope it helps
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