A cone has a volume of 47.1 cm³ and a radius of 3 cm what is its height?

Radius of cone ( r ) = 3 cm,

Curved surface area of a cone= 47.1 cm²

Curved surface area of a cone= πrl

47.1 = πrl

47.1 = 3.14 × 3 × l

l = 47.1 / (3.14 × 3)

l = 15.7 / 3.14= 1570/314= 5 cm

slant height (l) = 5 cm

Height of a cone (h) = √(l²) - (r²)

h = √ 5² -3²

h = √ 25 - 9 = √ 16 = 4 cm

h = 4 cm

Volume of cone= ⅓(πr²h)

= ⅓(3.14 × 3 × 3 × 4)

= 3.14 × 12= 37.68 cm³

Hence, the volume of a cone is 37.68 cm³.