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.