Mathematics

The height and the radius of the base of a cylinder are in the ratio 3 : 1. If its volume is 1029 π cm³; find its total surface area.

7 Likes

Given,

The ratio between height and radius of a cylinder = 3 : 1

Volume = 1029π cm³ …………..(1)

Let the radius of the base = r

Then, it’s height will be = 3r.

By formula,

Volume = πr²h …………. (2)

From (1) and (2), we get

⇒ πr²h = 1029π

⇒ r² × 3r = 1029

⇒ r³ = $\dfrac{1029}{3}$

⇒ r³ = 343

⇒ r = $\sqrt[3]{343}$

⇒ r = 7 cm.

Thus, radius = r = 7 cm and height = 3r = 3 x 7 = 21 cm.

By formula,

Total surface area = 2πr(h + r)

= 2 x $\dfrac{22}{7}$ x 7 x (21 + 7)

= 2 x 22 x 28

= 1232 cm².

Hence, total surface area of cylinder = 1232 cm².

Answered By

2 Likes