Area integralR integral 1 dA 8 integral integral 1 dA 8 m

Area = integral_R integral 1 dA = 8 integral integral 1 dA = 8 middot integral_0^pi/4 integral_0^2cos(2theta) 1 middot ridrdo a) Change sphere to radius ? Do you get twice as much? Take a pi/6 cone, do you get twice as much?

Solution

a.) When we will change radius to 2r, yes we will get area 2 times. Because as radius doubles, in same equation 2 will come out So, in place of 8 it will beconme 16 and rest equation will be same which is 2 times of actual area.

b.) Taking theta as pi/6, No we wont get area 2 times.