The total surface area of a solid metallic hemisphere is 462 cm². This is melted and moulded into a right circular cone. If the radius of the base of the cone is the same as that of the hemisphere, then its height is: (use $π =\frac{22}{7}$)

14 cm

We know that,

The Surface area of the Hemisphere = 3πr²

The volume of the hemisphere = \(\frac{2}{3}\) πr³

The volume of cone = \(\frac{1}{3}\) πr²h

We have,

The total surface area of a solid metallic hemisphere = 462 cm2.

The radius of the base of the cone = The same as that of the hemisphere

The Surface area of the Hemisphere =

= 462=3 × \(\frac{22}{7}\) × r²

= r² = 7 x 7

= r = 7 cm

 The volume of the Hemisphere = Volume of a cone

=  \(\frac{2}{3}\) πr³=\(\frac{1}{3}\) πr²h

= 2r=h

= h = 2 x 7 = 14 cm