61). A cylindrical box of radius 5 cm contains 10 solid spherical balls, each of radius 5 cm. If the top most ball touches the upper cover of the box, then volume of the empty space in the box is
| A). \( \Large \frac{2500}{3} \pi cm^{3} \) |
| B). \( \Large 5000 \pi cm^{3} \) |
| C). \( \Large 2500 \pi cm^{3} \) |
| D). \( \Large \frac{5000}{3} \pi cm^{3} \) |
|
62). What part of a ditch 48 m long, 16.5 m broad and 4 m deep can be filled by the earth got by digging a cylindrical tunnel of diameter 4 m and length 56 m?
| A). \( \Large \frac{1}{9} \) |
| B). \( \Large \frac{2}{9} \) |
| C). \( \Large \frac{7}{9} \) |
| D). \( \Large \frac{8}{9} \) |
|
63). The floor of a rectangular hall has a perimeter 250 m. If the cost of painting the four walls at the rate of Rs.10 per sq m is Rs.15000, then find the height of the hall.
| A). 8 m |
| B). 6 m |
| C). 9 m |
| D). 7 m |
|
64). A cylinder is surmounted by a cone at one end, a hemisphere at the other end. The common radius is 3.5 cm, the height of the cylinder is 6.5 cm and the total height of the structure is 12.8 cm. The volume V of the structure lies between
| A). 370 \( \Large cm^{3} \) and 380 \( \Large cm^{3} \) |
| B). 380 \( \Large cm^{3} \) and 390 \( \Large cm^{3} \) |
| C). 390 \( \Large cm^{3} \) and 400 \( \Large cm^{3} \) |
| D). None of the above |
|
65). The Side of a cube measures 9 cm. What will be the diagonal of the cube (in cm)?
| A). \( \Large 5\sqrt{3} \) |
| B). \( \Large 7\sqrt{3} \) |
| C). \( \Large 9\sqrt{3} \) |
| D). \( \Large 3\sqrt{3} \) |
|
66). The diagonal of a cube is \( \Large 2\sqrt{3} \) cm. Find the surface area of the cube.
| A). 15 sq cm |
| B). 18 sq cm |
| C). 25 sq cm |
| D). 24 sq cm |
|
67). The volume of a cuboid is 1989 \( \Large cm^{3} \), While its length and breadth are 17.cm and 13 cm, respectively. Find the height of the cuboid.
| A). 9 cm |
| B). 4 cm |
| C). 14 cm |
| D). 7 cm |
|
68). Three cubes of sides 1 cm, 6 cm and 8 cm are melted to form a new cube. Find half 0f the surface area of the new cube.
| A). 243 sq cm |
| B). 463 sq cm |
| C). 486 sq cm |
| D). 293 sq cm |
|
69). A metal box measures 20 cm x 12 cm x 5 cm. Thickness of the metal is 1 cm. Find the volume of the metal required to make the box.
| A). \( \Large 550 cm^{3} \) |
| B). \( \Large 656 cm^{3} \) |
| C). \( \Large 660 cm^{3} \) |
| D). \( \Large 475 cm^{3} \) |
|
70). How many cubes of 3 cm edge can be cut out of a cube of 18 cm edge?
| A). 63 |
| B). 432 |
| C). 216 |
| D). None of these |
|
