Question

A manufacturer plans to construct a cylindrical can to hold one cubic metre of liquid . If yhe cost of constructing the top and bottom of the can is twice the cost of constructing the curved side . What can be the dimensions of the most economical can ?

Answer 1

Answer: 2 (1/2π) ¹/³m

Step-by-step explanation:

Volume = πr²h= 1m³

Cost of top + bottom = a. (2πr²)

Cost of curved surface area  = a. (2πrh)

According to the question the cost of construction the top and bottom of the can is twice the cost of construction the curved side. So,

2 { a(2πr²)} = a (2πrh)

4πr² = 2πrh

2r = h

Height of can = 2 radius of can

πr²h  = 1

πr².2r =1

r³ = 1/ 2π

r = (1/2π) ¹/³

h = 2r = 2 (1/2π) ¹/³m

So, the answer is 2 (1/2π) ¹/³m