a-maths~~~~~~~~

(1)(a)
r+h = 15 => h = 15-r
V = πr^2h/3
= πr^2(15-r)/3
(b) differentiate w.r.t. r
dV/dr = π[2r(15-r) + (-1)r^2]/3
= π (30r - 3r^2)/3
= π (10r - r^2)
set dV/dr = 0, π(10r - r^2) = 0
r (10 -r) = 0
r = 10 or r= 0 (reject)
when r = 10+, dV/dr < 0
when r = 10-, dV/dr > 0
The volume attains the maximum value when r = 10
when r = 10, h = 15-10 = 5
Volumne = π(10)^2(15-10)/3 = 523.6sq. units