Vardaan Learning Institute

1. The area of a trapezium is $34 \text{ cm}^2$ and the length of one of the parallel sides is 10 cm and its height is 4 cm. Find the length of the other parallel side.

2. The diagonal of a quadrilateral shaped field is 24 m and the perpendiculars dropped on it from the remaining opposite vertices are 8 m and 13 m. Find the area of the field.

3. Find the total surface area of a closed cylindrical petrol storage tank that is 4.2 m in diameter and 4.5 m high.

4. A cuboid is of dimensions $60 \text{ cm} \times 54 \text{ cm} \times 30 \text{ cm}$. How many small cubes with side 6 cm can be placed in the given cuboid?

5. Find the height of the cylinder whose volume is $1.54 \text{ m}^3$ and diameter of the base is 140 cm.

6. A flooring tile has the shape of a parallelogram whose base is 24 cm and the corresponding height is 10 cm. How many such tiles are required to cover a floor of area $1080 \text{ m}^2$? (If required you can split the tiles in whatever way you want to fill up the corners).

7. An ant is moving around a few food pieces of different shapes scattered on the floor. For which food-piece would the ant have to take a longer round? Remember, circumference of a circle can be obtained by using the expression $C = 2 \pi r$, where $r$ is the radius of the circle.
(a) A Semicircle with diameter 2.8 cm
(b) A shape with 2.8 cm rounded on one side like a semicircle and straight lines forming a 'D' shape boundary.

8. Daniel is painting the walls and ceiling of a cuboidal hall with length, breadth and height of 15 m, 10 m and 7 m respectively. From each can of paint $100 \text{ m}^2$ of area is painted. How many cans of paint will he need to paint the room?

9. A godown is in the form of a cuboid of measures $60 \text{ m} \times 40 \text{ m} \times 30 \text{ m}$. How many cuboidal boxes can be stored in it if the volume of one box is $0.8 \text{ m}^3$?

10. A rectangular paper of width 14 cm is rolled along its width and a cylinder of radius 20 cm is formed. Find the volume of the cylinder. (Take $\pi = \frac{22}{7}$).

11. A rectangular piece of paper 11 cm x 4 cm is folded without overlapping to make a cylinder of height 4 cm. Find the volume of the cylinder.

12. The lateral surface area of a hollow cylinder is $4224 \text{ cm}^2$. It is cut along its height and formed a rectangular sheet of width 33 cm. Find the perimeter of rectangular sheet.

13. A road roller takes 750 complete revolutions to move once over to level a road. Find the area of the road if the diameter of a road roller is 84 cm and length is 1 m.

14. A company packages its milk powder in cylindrical container whose base has a diameter of 14 cm and height 20 cm. Company places a label around the surface of the container (as in the figure). If the label is placed 2 cm from top and bottom, what is the area of the label.

15. Water is pouring into a cubiodal reservoir at the rate of 60 liters per minute. If the volume of reservoir is $108 \text{ m}^3$, find the number of hours it will take to fill the reservoir.