the area of a circle is increased by 22 cm when its radius is increased by 1 cm?

Question

find the original radius of the circle

Answer 1

pi * (r + 1)(r + 1) - pi * r*r = 22
pi(r^2 + 2r + 1 + r^2) = 22
pi(2r + 1) - 22 = 0

Here I am going to simplify to 2 decimal places. 22/pi ~= 7.
pi(2r + 1 - 7) = 0
2r - 6 = 0
2r = 6
r = 3

Answer 2

The original circle has a radius r and the secon has a radius r+1

pi (r+1)^2 = pir^2 +22cm^2

pir^2 +2pi r +1 =pir^2 +22 so 2pi r= 21 and r = 21/2pi cm

Answer 3

no dear
area is measured in sqcms
when r=r+1
area becomes pi(r+1)2 from pir2
how many times it increases depends on radius

Answer 4

volume of water is 10/4 • π • 3² = 45π/2 volume of sphere is 4/3 • π • 3³ = 36π volume of glass up to height of sphere is 6 • π • 3² = 54π so space in glass left over by sphere (up to its height) is 54π – 36π = 18π so there's 22½ π – 18π = 4½ π cm³ of water to fill space above the sphere. divide that by the cross section of the cylinder, 9π, get height of 0.5 cm above top of sphere, so water rose from a height of 2.5 cm to a height of 6.5 cm, an increase of exactly 4.0 cm. cute problem. less water, we'd have needed calculus.

Answer 5

differentiating area we get da/dr=2pie r
now lhs =22 hence r=22/2/22/7
=7/2units

Answer 6

r = original radius

r + 1 = pi * 2r + 22
r = pi * 2r + 21
(Solve it.)

Answer 7

pi*[(r+1)^2]=pi*r^2 + 22.
Hence, 2*pi*r + pi=22.
Hence, r=22/(2*pi)=11/pi=3.5014cm

Answer 8

Ms.Chanda, I think something is wrong in your question.If it is area then it should be square cm.Or did you meant Perimetre??

Answer 9

6cm

opps, i mean 3