41). If the radius of a sphere is increased by 3%, then what per cent increase takes place in surface area of the sphere?
| A). 6.09% |
| B). 7% |
| C). 5.06% |
| D). 9% |
|
42). If radius of a sphere is decreased by 24%, by what per cent does its surface area decrease?
| A). 44% |
| B). 49% |
| C). 42.24% |
| D). 46.20% |
|
43). A prism has the base a right angled triangle whose sides adjacent to the right angle are 10 cm and 12 " cm long. The height of the prism is 20 cm. The dens1t of the material of the prism is 6 g/cu cm. The weight of the prism is
| A). 3.4 kg |
| B). 4.8 kg |
| C). 6.4 kg |
| D). 7.2 kg |
|
44). The base of a right prism is a right angled angled isosceles triangle whose hypotenuse is 'a' cm. If the height of the prism is 'h' cm, then its volume is
| A). \( \Large \frac{a^{2}h}{4} cm^{3} \) |
| B). \( \Large \frac{a^{2}h}{6} cm^{3} \) |
| C). \( \Large \frac{a^{2}h}{8} cm^{3} \) |
| D). \( \Large \frac{a^{2}h}{12} cm^{3} \) |
|
45). The base of a cone and a cylinder have the same radius 6 cm. They have also the same height 8 cm. The ratio of the curved surfaces of the cylinder to that of the cone is
| A). 4 : 3 |
| B). 5 : 3 |
| C). 8 : 5 |
| D). 8 : 3 |
|
46). A solid metallic cylinder of base radius 3 cm and height 5 cm is melted to form cones, each of height 1 cm and base radius 1 mm. The number of cones is
| A). 7500 |
| B). 13500 |
| C). 3500 |
| D). 4500 |
|
47). A solid consists of circular cylinder with exact fitting right circular cone placed on the top. The height of the cone is h. If total volume of the solid is three times the volume of the cone, then the height of the circular cylinder is
| A). 2 h |
| B). \( \Large \frac{2 h}{3} \) |
| C). 4 h |
| D). \( \Large \frac{3 h}{2} \) |
|
48). The volumes of a sphere and a right circular cylinder having the same radius are equal. The ratio of the diameter of the sphere to the height of the cylinder is
| A). 1 : 2 |
| B). 2 : 1 |
| C). 2 : 3 |
| D). 3 : 2 |
|
49). A cylindrical jar, whose base has a radius of 15 cm, is filled with water upto a height of 20 cm. A solid iron spherical ball of radius 10 cm is dropped in the jar to submerge completely in water. Find the increase in the level of water (in cm).
| A). \( \Large 5\frac{17}{27} \) |
| B). \( \Large 5\frac{5}{27} \) |
| C). \( \Large 5\frac{8}{9} \) |
| D). \( \Large 5\frac{25}{27} \) |
|
50). A sphere of radius r has the same volume as that of a cone with a circular base of radius r. Find the height of the cone.
| A). 2r |
| B). \( \Large \frac{r}{3} \) |
| C). 4r |
| D). \( \Large \left(\frac{2}{3}\right)r \) |
|
