Chapter 11: Mensuration
Ex 11.1
1. A square and a rectangular field with measurements as given in the figure have the same perimeter. Which field has a larger area?
2. Mrs Kaushik has a square plot with the measurement as shown in the figure. She wants to construct a house in the middle of the plot. A garden is developed around the house. Find the total cost of developing a garden around the house at the rate of ` 55 per m²
3. The shape of a garden is rectangular in the middle and semi-circularat the ends as shown in the diagram. Find the area and the perimeterof this garden [Length of rectangle is20 – (3.5 + 3.5) metres].
4. 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 area of 1080 m²?
(If required you can split the tiles in whatever way you want to fill up the corners).
5. 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, a circumference of a circle can be obtained by using the expression c = 2πr, where r is the radius of the circle.
Ex 11.1 Complete Free pdf Download
Ex 11.2 Mensuration
1. The shape of the top surface of a table is a trapezium. Find its areaif its parallel sides are 1m and 1.2 m and the perpendicular distancebetween them is 0.8 m.
2. The area of a trapezium is 34 cm² and the length of one of the parallel sides is10 cm and its height is 4 cm. Find the length of the other parallel side.
3. Length of the fence of a trapezium-shaped field ABCD is 120 m. IfBC = 48 m, CD = 17 m and AD = 40 m, find the area of this field. SideAB is perpendicular to the parallel sides AD and BC.
4. The diagonal of a quadrilateral-shaped field is 24 mand the perpendiculars dropped on it from theremaining opposite vertices are 8 m and 13 m. Findthe area of the field.
5. The diagonals of a rhombus are 7.5 cm and 12 cm. Find its area.
6. Find the area of a rhombus whose side is 5 cm and whose altitude is 4.8 cm.If one of its diagonals is 8 cm long, find the length of the other diagonal.
7. The floor of a building consists of 3000 tiles which are rhombus shaped and each ofits diagonals are 45 cm and 30 cm in length. Find the total cost of polishing the floor,if the cost per m² is ₹4.
8. Mohan wants to buy a trapezium shaped field.Its side along the river is parallel to and twicethe side along the road. If the area of this field is10500 m² and the perpendicular distancebetween the two parallel sides is 100 m, find thelength of the side along the river.
9. Top surface of a raised platform is in the shape of a regular octagon as shown inthe figure. Find the area of the octagonal surface.
10. There is a pentagonal shaped park as shown in the figure.For finding its area Jyoti and Kavita divided it into two different ways
11. Diagram of the adjacent picture frame has outer dimensions = 24 cm × 28 cmand inner dimensions 16 cm × 20 cm. Find the area of each section ofthe frame, if the width of each section is same.
Ex 11.2 Mensuration Free PDF Download
Ex 11.3
1. There are two cuboidal boxes shown in the adjoining figure. Which box requires a lesser amount of material to make?
2. A suitcase with measures 80 cm × 48 cm × 24 cm is to be covered with a tarpaulin cloth. How many metres of tarpaulin of width 96 cm is required to cover 100 such suitcases?
3. Find the side of a cube whose surface area is 600 cm².
4. Rukhsar painted the outside of the cabinet of measure 1 m × 2 m × 1.5 m. How much surface area did she cover if she painted all except the bottom of the cabinet?
5. 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 m² of area is painted. How many cans of paint will she need to paint the room?
6. Describe how the two figures at the right are alike and how they are different. Which box has a larger lateral surface area?
7. A closed cylindrical tank of radius 7 m and height 3 m is made from a sheet of metal. How many sheets of metal are required?
8. The lateral surface area of a hollow cylinder is 4224 cm² It is cut along its height and formed a rectangular sheet of width 33 cm. Find the perimeter of a rectangular sheet?
9. 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 the length is 1 m.
10. A company packages its milk powder in a cylindrical container whose base has a diameter of 14 cm and a height of 20 cm. The company places a label around the surface of the container (as shown in the figure). If the label is placed 2 cm from top and bottom, what is the area of the label?
Ex 11.3 Mensuration Free PDF Download
Ex 11.4
1. Given a cylindrical tank, in which situation will you find surface area and in which situation volume.
(a) To find how much it can hold.
(b) Number of cement bags required to plaster it.
(c) To find the number of smaller tanks that can be filled with water from it.
2. Diameter of cylinder A is 7 cm, and the height is 14 cm. The diameter of cylinder B is 14 cm and height is 7 cm. Without doing any calculations can you suggest whose volume is greater?
Verify it by finding the volume of both cylinders.
Check whether the cylinder with greater volume also has a greater surface area?
3. Find the height of a cuboid whose base area is 180 cm² and volume is 900 cm³?
4. A cuboid is of dimensions 60 cm × 54 cm × 30 cm. How many small cubes with sides 6 cm can be placed in the given cuboid?
5. Find the height of the cylinder whose volume is 1.54 m³ and the diameter of the base is 140 cm ?
6. A milk tank is in the form of cylinder whose radius is 1.5 m and length is 7 m. Find the quantity of milk in litres that can be stored in the tank?
7. If each edge of a cube is doubled, (i) how many times will its surface area increase? (ii) how many times will its volume increase?
8. Water is pouring into a cubiodal reservoir at the rate of 60 litres perminute. If the volume of reservoir is 108 m3, find the number of hours itwill take to fill the reservoir.
Ex 11.4 Free PDF Download
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