A solid metallic rectangular block of dimensions 112 cm × 44 cm × 25 cm is melted and recast into a cylinder of radius 35 cm. The curved surface area (in cm²) of the cylinder is: (Take π = 22/7)

Given:

Dimensions of the metallic rectangular block is 112 cm × 44 cm × 25 cm

Radius of the cylinder = 35 cm

Concept used:

Volume of a cuboid = l × b × h

Volume of a cylinder = πr²h

Curved surface area of the cylinder = 2πrh

Here,

l = length

b = breadth

h = height

r = radius

h = height

Calculation:

Let the height of the cylinder be h

According to the question,

112 × 44 × 25 = (22/7) × 35² × h

⇒ (112 × 44 × 25 × 7)/(22 × 35 × 35) = h

⇒ h = 32

So, the height of the cylinder = 32 cm

Now,

Curved surface area of the cylinder = 2 × (22/7) × 35 × 32

⇒ 44 × 5 × 32

⇒ 7040

∴ The curved surface area (in cm2) of the cylinder is 7040.