Determining a formula for the change in surface area of a uniform solid sphere of radius r if it's Coefficient of linear expansion is a (assumed constants )and its temperature is changed by DT ​

Explanation:

Area A = 4 pi R^2

lnA = ln(4 pi) + 2 ln R

dA/A = 2 dR/R = 2*(alpha)*dT

delta A = 2A*alpha*(delta T)

OR

A at T + deltaT

delta A = 4 pi (R + deltaR)^2 - A

= 4 pi R(1 + alpha*deltaT)^2 -A

= 4 pi R^2 *[1 + 2*alpha*deltaT +

(alpha*deltaT)^2] - A

= 2*A*alpha*deltaT + A*(alpha*deltaT)^2

(Ignore the second term in deltaT^2)

54 degrees incident angle = reflected angle

angle is from normal turned to line of ray