Class 8 Maths

# Mensuration

## Exercise 11.3

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

**Answer:** Volume of the Cuboid = l x b x h

= 60 x 40 x 50 = 12000 cubic cms

Volume of Cube = Side^{3}

=50^{3} = 125000

As the volume of the cube is greater than that of the cuboid so it will require more material, and the cuboid will require less material

Question 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?

**Answer:** Surface Area of Cuboid = 2(lb + lh + bh)

= 2 (80 x 48 + 80 x 24 + 48 x 24)

= 2(3840 + 1920 + 1152)

= 2 x 6912 = 13824

Hence, Surface Area of 100 suitcases = 1382400 sq cms

Required tarpaulin will have same area

Question 3: Find the side of a cube whose surface area is 600 cm^{2}.

**Answer:** Surface Area = 6 x side^{2}

Or, 600 = 6 x side^{2}

Or, Side^{2} = 100

Or, Side = 10 cm

Question 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.

**Answer:** Surface Area of Cabinet = 2(lb + lh + bh)

= 2(1 x 2 + 1 x 1.5 + 1.5 x 2)

= 2(2 + 1.5 + 3) = 2 x 6.5 = 13

Area of Bottom Surface = 1 x 2 = 2 sq m

Hence, Area Covered by painting = 13-2 = 11 sq m

Question 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?

**Answer:** Area of All walls, ceilings and floor = 2(lb + lh + bh)

= 2(15 x 10 + 15 x 7 + 10 x 7)

= 2(150 + 105 + 70)

= 2 x 325 = 650

Area of Floor = 15 x 10 = 150

Hence, Painted Area =650-150=500

As, one can of paint is enough for 100 sq m

So, 500/100 = 5 cans are needed to paint the hall.

**Alternate Method:** Area of Walls of a Room = 2 x h x (l + b)

= 2 x 7 x (15 + 10)

= 14 x 25 = 350

Area of Roof = Area of Floor = 150

Total Area to be painted = 350+150=500

Question 6: Describe how the two figures given below are alike and how they are different. Which box has larger lateral surface area?

**Answer:Similarity:** Their dimensions are equal

**Difference:**The figure on the left is cylindrical and that on the right is cuboidal.

It is clear that the cylinder is having a larger surface area.

Question 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?

Question 8: The lateral surface area of a hollow cylinder is 4224 cm^{2}. It is cut along its height and formed a rectangular sheet of width 33 cm. Find the perimeter of rectangular sheet?

**Answer:** Area of Rectangular Sheet = Surface Area of the Cylinder

Area of Rectangle = l x b

Or, l x b = 4224

l x 33 = 4224

Question 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.

**Answer:** In one revolution the wheel of the roller will cover an area equal to its surface area.

Question 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.

**Answer:** The cylindrical area covered by the label will have

height = 20-4 = 16 cms