Answer: r ≈ 5.95
Step-by-step explanation:
Let S be the surface area , then
S = + r
Differentiating S with respect to r , we have
dS = dr + dh
= (2r + + ) dr + dh
For the area to remain the same it means dS = 0
since r = 6cm , h = 8cm , dh = 0.28 then we have
0 = (12π + 10π +)dr + X 0.28.
Making dr the subject of formula , we have
(12π + 10π +)dr = - ( X 0.28)
() dr = -
(640)dr = - 33.6
dr = - 33.6 / 640
dr = 0.05
This means that the radius should decrease by 0.05 for the area to remain the same. That means the radius = 6 - 0.05
r ≈ 5.95