Mensuration
Exercise 3
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
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
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
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 = 132 = 11 sq m
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 =650150=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
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.
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?
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
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.
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 = 204 = 16 cms
