Mensuration means measurement. It is being done in our life in many situations. For example, Length of cloth we need for stitching, the area of a wall which is being painted, perimeter of a rectangular plot to be fenced, quantity of water needed to fill the tank etc. For these kinds of activities, we are doing measurements for further needs.
Here, we cover three areas
1. Perimeter 2. Area 3. Volume
To find these things we have to remember the formulae of plane figures and solid figures. Try to understand the concept behind reaching the formula.
1. The area of a rectangular plate is 236.25 sq.cm. If the length of the plate is 17.5 cm, find the perimeter of the plate.
Ans. 62 cm
2. The breadth of a rectangular plot is 75% of its length. If the perimeter of the plot be 1050 m, what is its area?
3. In measuring the sides of a rectangle, one side is taken 10% in excess, and the other 5% in deficit. What is the change in its area as a percentage?
4. How many tiles of 20 cm length and 10 cm width are required to pave the floor of a room 8 m long and 5 m wide?
5. The circumference of two circles is 88 metre and 132 metre respectively. What is the difference between the area of the larger circle and the smaller circle?
Ans. 770 sq.m
6. A solid metallic spherical ball of radius 7 cm is melted down and recast into small cones. If the diameter of the base of the cone is 14 cm and the height is 2 cm, find the number of such cones can be made.
7. A hall is 10 metres long and 8 metres wide. What will be the cost of carpeting the room if 0.5 metres of space is left around the room? The rate of 0.25 metre wide carpet is Rs.20 per metre.
8. A square field has an area of 50625 sq. m. Find the cost of fencing around it at Rs.15 per metre.
9. Cost of fencing a circular plot at the rate of Rs.12 per metre is Rs.2,640. What will be the cost of carpeting the floor of the plot at the rate of Rs.85 per square metre?
10. A circle and a rectangle have the same perimeter. The sides of the rectangle are 18 cm and
26 cm. What will be the area of the circle?
1) 88 cm2 2) 1250 cm2 3) 154 cm2 4) 128 cm2 5) None of these
Ans. None of these
11. A circular garden has a 7 m wide road around the border. Find the cost of leveling the road at Rs.5 per square meter if the radius of the inner circle is 21 m?
12. The lateral surface area of a cylinder is thrice the area of its base. Find the ratio of its height and the base radius?
Ans. 3 : 2
13. Two cubes have their volumes in the ratio 8 : 27. Find the ratio of their surface areas.
Ans. 4 : 9
14. A horse is tied with a 14 m long rope. How much ground will it be able to graze?
1) 125 Sq.m 2) 275 Sq.m 3) 625 Sq.m 4) 675 Sq.m 5) None of these
Ans. None of these
15. Find the length of the longest stick that can be placed in a room of 12 m long, 9 m broad and 8 m high.
Ans. 17 m
16. A field is 375 m long and 40 m broad. A tank 30 m long, 20 m broad and 12 m deep is dug in the field and earth taken out of it and is spread equally over the field. How much is the level of field raised?
Ans. 50 cm
17. A rectangular field of 60-metre length and 40 metres wide is to be surrounded by a road 5 meter wide. If the cost of making 1 square meter road is Rs.500, what would be the cost of the entire road?
18. A room is 7.5 m long, 5.5 m broad and 5 m high. What will be the expenditure in covering the walls by paper 40 cm broad at the rate of 75 paise per meter?
19. The length and breadth of a rectangle increased by 20% and 10% respectively. How much percent will its area be increased?
20. 7 cm radius and 28 cm height solid metallic cylinder is melted and recast into small spherical balls of 7 cm radius. Find the number of cubes that can be made.