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 $π =\frac{22}{7}$)
Answer & explanation
Correct answer: option 1
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