Given:

Height of the cone = 21 cm

Formula used:

Curved surface area of a right circular cone = πrl

Volume of a cone = \(\left( {\frac{1}{3}} \right) \times {\rm{\pi }} \times {{\rm{r}}^2} \times {\rm{h}}\)

Area of circle = πr²

\({\rm{h}} = {\rm{\;}}\sqrt {{{\rm{l}}^{2{\rm{\;}}}} - {\rm{\;}}{{\rm{r}}^2}} \)

Where r = radius, l = slant height, h = height of a cone

Calculation:

According to the question,

πrl = 3πr²

⇒ l = 3r

⇒ l/r = 3/1

\({\rm{h}} = {\rm{\;}}\sqrt {{{\rm{l}}^{2{\rm{\;}}}} - {\rm{\;}}{{\rm{r}}^2}} \)

⇒ \({\rm{h}} = {\rm{\;}}\sqrt {{{\rm{3}}^{2{\rm{\;}}}} - {\rm{\;}}{{\rm{1}}^2}} \)

⇒ \({\rm{h}} = {\rm{\;}}\sqrt {{{\rm{9}{\rm{\;}}}} - {\rm{\;}}{{\rm{1}}}} \)

⇒ h = √8

⇒ h = 2√2

⇒ 21 = 2√2

⇒ r = 21/2√2

\(\left( {\frac{1}{3}} \right) \times {\rm{\pi }} \times {{\rm{r}}^2} \times {\rm{h}}\) = \(\left( {\frac{1}{3}} \right) \times {\frac{22}{7}} \times ({{\frac{21}{2\sqrt 2}})^2} \times {\rm{21}}\) 

⇒\(\left( {\frac{1}{3}} \right) \times {\frac{22}{7}} \times ({{\frac{441}{8}})} \times {\rm{21}}\)

⇒ 22 × 63/8 × 7

⇒ 1212.75

⇒ Volume = 1212.75 cm³ ≈ 1213 cm³

∴ Volume of the cone is 1213 cm³