InterviewSolution
Saved Bookmarks
InterviewSolution
| 1. |
A company deals in casting and moulding of metal on orders received from its clients.In one such order, company is supposed to make 50 toys in the form of a hemisphere surmounted by a right circular cone of the same base radius as that of hemisphere. If the radius of the base of the cone is 21 cm and height is 28 cm,(a) find the volume of 50 toys;(b) find the ratio of the volume of hemisphere to the volume of cone. |
|
Answer» r = 21 cm h = 28 cm (a) Volume of 1 toy = Volume of cone + Volume of hemisphere \(=\frac13\pi r^2h+\frac23\pi r^3\) \(= \frac13\pi r^2(h + 2r)\) \(= \frac13 \times\frac{22}{7}\times 21\times21\,(28 + 42)\) = 462 x 70 = 32340 cm3 \(\therefore\) Volume of 50 toys = 32340 x 50 cm3 = 1617000 cm3 (b) \(\frac{Volume \,of\, hemisphere}{Volume \, of \, circle} =\cfrac{\frac23\pi r^3}{\frac13\pi r^2h}\) \(=\frac{2r}{h}\) \(=\frac{2\times21}{28}\) \(=\frac32\) = 3 : 2 Hence, required ratio is 3 : 2. |
|