Saved Bookmarks
| 1. |
The surface area of a sphere of radius 5 cm is five times the area of the curved surface of a cone of radius 4 cm. Find the height and the volume of the cone. |
|
Answer» Surface area of the sphere = 4π × 5 × 5 cm2 . Curved surface area of the cone = π × 4 × l cm2, where l is the slant height of the cone. According to the statement 4π × 5 × 5 = 5 × π × 4 × l or l = 5 cm. Now, l2 = h2 + r2 Therefore, (5)2 = h2 + (4)2 where h is the height of the cone or (5)2 – (4)2 = h2 or (5 + 4) (5 – 4) = h2 or 9 = h2 or h = 3 cm Volume of Cone = 1/3 πr2 h = 1/3 x 22/7 x 4 x 4 x 3 cm3 = (22 x 16)/7 cm3 = 352/7 cm3 = 50.29 cm3 |
|