Question

the base area of a right cylinder is 16pie centimetre cube.its height is 5 cm, then the curved surface area is ________.​

Answer 1

Answer

Let radius of base of cylinder is r and height is h

Then, volume of cylinder , V = π r²h = 16π

r² h = 16 ⇒h = 16/r² ------(1)

Now, surface area of cylinder , S = 2πrh + 2πr²

S = 2πr × 16/r² + 2πr² [ from equation (1) ]

S = 32π/r + 2πr²

Now, differentiate with respect to r

dS/dr = -32π/r² + 4πr , dS/dr = 0 ⇒r ³ = 8

r = 2 , check at r = 2 d²S/dr²

d²S/dr² = -64π/r³ + 4π = -8π + 4π < 0 hence, at r =2 , Surface area, S will be minimum .

Now, height = 16/r² = 16/4 = 4 cm

Hence, height = 4cm

Answer 2

Question

the base area of a right cylinder is 16pie centimetre cube.its height is 5 cm, then the curved surface area is ________.

Answer

refer to the attachment!!

Hope it helps you ♥️