Question

Three rectangles A₁, A₂ and A₃ have the same area. Their lengths a₁, a₂ and a₃ respectively are such that a₁ < a₂ < a₃. Cylinders C₁, C₂ and C₃ are formed from A₁, A₂ and A₃ respectively by joining the parallel sides along the breadth. Then,

(a) C₁ will enclose maximum volume.

(b) C₂ will enclose maximum volume.

(c) C₃ will enclose maximum volume.

(d) Each of C₁, C₂ and C₃ will enclose equal volume.

Answer 1

Correct option is (c) C₃ will enclose maximum volume.

The volume of a cylinder is V = πr²h

We know that the height of cylinder are in order, a_1​ < a₂​ < a₃​.

Since the volume of a cylinder is directly proportional to its height, the maximum volume will be enclosed by cylinder C_3​.