Question

the height and radius of base of a cylinder
are in ratio 3 is to 1 if its
Volume is 1029 piecm3. Find
its TSA​

Answer 1

Ratio of h and r = 3 : 1

Let the height and radius of base be (3x) and (x) respectively.

Volume = 1029π cm³

We know,

Volume of a right circular cylinder = πr²h

∴ πr²h = 1029π

⇒ (x)²(3x) = 1029

⇒ 3x³ = 1029

⇒ x³ = 343

⇒ x = 7.

Now, TSA of cylinder = 2πr(r + h)

∴ TSA = 2πx(x + 3x)

⇒ TSA = 2π(4x²)

⇒ TSA = 8πx² = 8π(7)²

⇒ TSA = 392π.

Hence, TSA of the cylinder is of (392π) cm².