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Chapter 9: Mensuration

    Introduction

    Area of a Polygon

    Solid Shapes

    Surface Area of Cube, Cuboid and Cylinder

    Volume of Cube, Cuboid and Cylinder

    Volume and Capacity

    Exercise 9.1

    Exercise 9.2

    Exercise 9.3

    What Have We Discussed?

    Enhanced Curriculum Support

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Chapter 9: Mensuration > Exercise 9.2

Exercise 9.2

1. There are two cuboidal boxes as shown in the adjoining figure. Which box requires the lesser amount of material to make?

Instructions

(a) Given: Length of cuboidal box (l) = 60 cm, Breadth of cuboidal box (b) = 40 cm and Height of cuboidal box (h) = 50 cm
Total surface area of cuboidal box =
Total surface area of box = 2 × ( × + × + × ) = 2 × ( + + ) = cm2
(b) Length of cubical box (l) = cm, Breadth of cubicalbox (b) = cm and Height of cubicalbox (h) = cm
Total surface area of cubical box =
Total surface area of box = × ( × ) = × =
From the result of (a) and (b), box requires the 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.

Instructions

Length of tarpaulin cloth

  • We know that, total surface area of suitcase of length(l), breadth(b) and height(h): unit2
  • Substituting the values we get, surface area of suitcase: cm2
  • We also know that Area of Tarpaulin cloth required = Surface area of 100 suitcase
  • This gives us the equation: 13824 x 100 = where l is length of the cloth.
  • Thus, the length of tarpaulin required: m.
  • We have found the required length.

3. Find the side of a cube whose surface area is 600 cm2.

Instructions

Surface area of cube = cm2
Surface area of a cube =
Thus, 6side2 = 600 i.e. side2 = (or) side = ±
Thus, the side length is 10 cm (since side cannot be negative)

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 ?

Cabinet

Instructions

Area of cabinet painted

  • The total area of cabinet painted: where l - length, b - breadth and h - height of cabinet
  • Substituting the values we get the surface area painted: m2
  • We have found the cabinet area painted.

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?

Instructions

Number of cans required ?

  • If l- length, b- breadth and h- height of the room, the area to be painted is:
  • Substituting the values
  • Area of room painted: m2
  • Calculating the number of cans
  • Thus, the number of paint cans required:
  • We have found the desired value.

6. Describe how the two figures are alike and how they are different: a right-angled cylinder of diameter 7 cm with height of 7 cm and a cube of side length 7cm. Which box has larger lateral surface area?

Instructions

Similarity: Both figures have the same and the same
Difference: The first figure has bottom and top while the second figure has bottom and top.
The first figure is a while the second figure is a .
Lateral surface area of cylinder = where radius (r) = cm and height (h) = cm
= 2 × × × = cm2
lateral surface area of cube = = × = cm2
Hence, the 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 much sheet of metal is required?

Instructions

Radius of cylindrical tank (r) = m and height of cylindrical tank (h) = m
Total surface area of cylindrical tank =
Total surface area of cylindrical tank = × × × (+) = × () = m2
Therefore, 440 m2 metal sheet is 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 rectangular sheet?

Instructions

Lateral surface area of hollow cylinder = 4224 cm2
We have: Width of rectangular sheet = cm and assume 'l' be the length of the rectangular sheet.
Lateral surface area of cylinder = Area of the rectangular sheet i.e. 4224 = b × l i.e. 4224 = 33 × l which gives l = 422433 = cm
So, the length of the rectangular sheet is 128 cm.
Perimeter of rectangular sheet = 2l+b = 2(+) = cm
The perimeter of the rectangular sheet is 322 cm.

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 length is 1 m.

Road Roller

Instructions

Finding area of road

  • The surface area of the roller: where r - radius and h - length of the roller
  • Substituting the values
  • Area of roller surface: m2
  • Area of the road = times the surface area of roller.
  • Total area of road: m2
  • We have found the area of the road made.

10. 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 shown in the figure). If the label is placed 2 cm from top and bottom, what is the area of the label?

Labelled bottle

Instructions

Finding label area

  • The area of the label: where r - radius and h - length of the roller
  • Calculating the height of the label, we get: h = cm
  • Substituting the values
  • Area of label: cm2
  • We have found the area of the label.