Saved Bookmarks
| 1. |
14. A cylindrical can, whose base is horizontal andof radius 3.5 cm, contains sufficient water sothat when a sphere is placed in the can, thewater just covers the sphere. Given that thesphere just fits into the can, calculate:(i) the total surface area of the can in contactwith water when the sphere is in it;(ii) the depth of water in the can before thesphere was put into the can. |
|
Answer» In the cylinderof radius R, the sphere just fits. So its radius is R. Volume of of cylinder up to the height 2R in the cylinder =πR² * 2R = 2π R³Volume of sphere = 4πR³/3 Volume of water in the gap between cylinder and sphere = 2πR³-4πR³/3 = 2πR³ /3 2) Depth of water in the can before sphere is put inside it = volume of water/area of cross section of can = (2π R³ / 3 )/π R² = 2 R/3 = 2 * 3.5 /3 = 7/3 cm 1) Surface area surface area of can in contact with water = flat surface + curved surface =πR² + 2π R * 2 R = 5π R² = 5 * 22/7 * 3.5² cm² = 110 /7 * (7/2)² cm² = 385 / 2 cm² |
|