Question

A solid cylinder has total surface area of 462 sq m.Its curved area is one third of its total surface area.Find the volume of the cylinder...

Answer 1

Answer : 539 m³

Solution :
_________

As we know that : Curved Surface Area of cylinder = 2πrh

Given that : Total Surface Area of cylinder = 462 m²

Also given that : the curved surface area of cylinder is one third of its TSA

Then, according to the question :

2πrh = 462×1/3 = 154 m² .....(1)

As we know that : Total Surface Area of cylinder = 2πrh+2πr²

Now, according to the question :

2πrh + 2πr² = 462

=> 154+2πr² = 462 [ from equation (1) ]

=> 2πr² = 308

=> 2×22/7×r² = 308

=> r = 7 m

From equation (1)

2πrh = 154

=> 2×22/7×7×h = 154

=> h = 3.5 m

Now, volume of cylinder = πr²h

=> Volume = 22/7×7×7×3.5

=> Volume = 539 m³

So, the volume will be 539 m³