A playground decoration is made by fixing a right circular cone onto the top of a…
MATHEMATICS · Multi-part · CBSE · Mathematics · Surface Areas and Volumes · Surface Areas and Volumes
Problem
A playground decoration is made by fixing a right circular cone onto the top of a vertical solid cylinder and then scooping out a hemisphere from the bottom of the cylinder, as described below:
• The cylinder has radius 7 cm and height 15 cm.
• The cone has the same base radius 7 cm and a height of 9 cm.
• The hemisphere removed has radius 7 cm and its flat face coincides with the base of the cylinder.
(i) Find the volume of the remaining solid after the hemisphere is removed.
(ii) Calculate the total outer surface area of the remaining solid, leaving out the circular face that was in contact with the removed hemisphere.
(iii) If the material of the solid weighs 5 g per cubic centimetre, find the total mass of the decoration. (Take π=22/7.)