The total surface area of a solid metallic hemisphere is 462 cm2. This is melted and molded 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 = 22/7)
Show answer & explanation
Correct answer: A
Explanation
The correct answer is Option 1 i.e. 14 cm.
Given that
The total surface area of a solid metallic hemisphere is 462 cm2.
If the radius of the base of the cone is the same as that of the hemisphere
We know that,
The total surface area of the hemisphere = 3πR2.
The volume of a hemisphere = (2/3)πR3 cubic units
The volume of a right circular cone = (1/3) × πr2h
where r is the radius of the base circle, R is the radius of the hemisphere and h is the height of the cone
According to the question
⇒ 3πR2 = 462
⇒ πR2 = 154
⇒ R = 7 cm
Volume of a hemisphere = Volume of a cone
⇒ (2/3)πR3 = (1/3) × πr2h
⇒ 2 × 73 = 72 h
⇒ h = 14 cm