Question

The curved surface area of a right circular cylinder of height \( 14 cm \) is \( 176 cm ^{2} \). Find the diameter of the base of the cylinder.

Answer 1

Given:

The curved surface area of a right circular cylinder, (C.S.A) = 176 cm²

Height of the cylinder (h) = 14 cm

Let, Radius of the cylinder be "r".

Since, Curved surface area of a right circular cylinder = 2πrh sq.units

\(\Rightarrow 2\pi rh = 176 \ cm^2\)

\(\Rightarrow 2 \times \frac{22}7 \times r \times h = 176 \ cm^2\)

\(\Rightarrow \frac{44}7 \times r \times 14\ cm = 176 \ cm^2\)

\(\Rightarrow r = \frac7{44} \times \frac 1{14\ cm }\times 176 \ cm^2\)

\(\Rightarrow r = \frac7{44} \times \frac 1{14\ cm }\times 176 \ cm^2\)

\(\Rightarrow r = \frac11 \times \frac 1{2 }\times4 \ cm\)

\(\Rightarrow r = 2\ cm\)

⇒ Diameter of the radius is 2 × r = 2 × 1 cm = 2 cm

Hence, Diameter of the radius is 2 cm.