the diameter of a circle is increased by 40% then is area is increased by
Answers
Answer:
40% increased is the new area.
Step-by-step explanation:
area is πr^2
Answer:
Area of circle increases by 96%
Step-by-step explanation:
Let r = radius of original circle
=> Area of circle = π*r²
If the diameter of the circle is increased by 40%, the radius will also increase by 40%. (See "More Explanation" below)
Radius of new circle = r + 40% of r
= r + 0.4*r
= 1.4*r
=> Area of new circle = π*(1.4*r)²
=π *(1.4)²*r²
=π * 1.96 * r²
Area of new circle = 1.96 * (πr²)
= 1.96 * (Area of old circle)
= (1 + 0.96) * Area of old circle
= Area of old circle + 0.96*Area of old circle
= Area of old circle + 96% of Area of old circle
Hence, the new circle will have 96% more area than the old circle. This means that if radius is increased BY 40%, the area increases BY 96%
More Explanation:
Old Diameter = d
Old radius = r
d = 2r
New diameter = 1.4d ..(increase of 40%)
= 1.4*2r
= 2.8r
New radius = (New diameter) ÷ 2
= 2.8r ÷ 2
= 1.4r (which means 40% more than r)
New radius is also 40% more than old radius