1. There are two cuboidal boxes as shown in the adjoining figure. Which box requires the lesser amount of material to make?
Length of cuboidal box (l) = 60 cm
Breadth of cuboidal box (b) = 40 cm
Height of cuboidal box (h) = 50 cm
According to question:
Total surface area of cuboidal box = 2×(lb + bh + hl)
= 2×(60×40 +40×50 + 50×60)
= 14800 cm2
Length of cubical box (l) = 50 cm
Breadth of cubical box (b) = 50 cm
Height of cubical box (h) = 50 cm
Total surface area of cubical box = 6(side)2
= 15000 cm2
Hence, according to the result of (a) and (b), we get that cuboidal box requires the lesser amount of material to make.
2. A suitcase with measures 80 cm x 48 cm x 24 cm is to be covered with a tarpaulin cloth. How many meters of tarpaulin of width 96 cm is required to cover 100 such suitcases?
Length of suitcase (l) = 80 cm,
Breadth of suitcase (b)= 48 cm
Height of cuboidal (h) = 24 cm
Total surface area of suitcase box = 2(lb+bh+hl)
= 2 (3840+1152+1920)
= 13824 cm2
Area of Tarpaulin cloth = Surface area of suitcase
l×b = 13824
l ×96 = 13824
l = 144
Required tarpaulin for 100 suitcases = 144×100
= 14400 cm = 144 m
Hence, required tarpaulin cloth to cover 100 suitcases is 144 m.
3. Find the side of a cube whose surface area is 600cm2.
Given, surface area of cube = 600 cm2
From formula we know that,
Surface area of a cube = 6(side)2
6(side)2 = 600
(side)2 = 100
side = ±10
Hence, side cannot be negative. So, the measure of each side of a cube is 10 cm.
4. Rukshar 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?
Length of cabinet (l) = 2 m
Breadth of cabinet (b) = 1 m
Height of cabinet (h) = 1.5 m
Surface area of cabinet except the bottom of the cabinet = lb+2(bh+hl)
= 11 m2
Hence, required surface area of cabinet is 11m2.
5. Daniel is paining 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?
Length of wall (l) = 15 m
Breadth of wall (b) = 10 m
Height of wall (h) = 7 m
Total Surface area of classroom except floor = lb+2(bh+hl )
= 500 m2
Total number of required cans = Area of classroom/Area of one can
= 500/100 = 5
Hence, 5 cans are required to paint the room.
6. Describe how the two figures below are alike and how they are different. Which box has larger lateral surface areas?
Diameter of cylinder (d) = 7 cm
So, radius of cylinder (r) = 7/2 cm [ r = d/2]
Height of cylinder (h) = 7 cm
Lateral surface area of cylinder = 2πrh
= 2 × (22/7) × (7/2) × 7
= 154 cm2
Lateral surface area of cube = 4 (side)2
= 196 cm2
Hence, the cube has 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?
Radius of cylindrical tank (r) = 7 m
Height of cylindrical tank (h) = 3 m
Total surface area of cylindrical tank = 2πr(h+r)
= 44×10 = 440 m2
Hence, 440 m2 metal sheet is required.
8. The lateral surface area of a hollow cylinder is 4224cm2. It is cut along its height and formed a rectangular sheet of width 33 cm. Find the perimeter of rectangular sheet?
Given, lateral surface area of hollow cylinder = 4224 cm2
Width of rectangular sheet (b) = 33 cm
Let l be the length of rectangular sheet.
Lateral surface area of cylinder = Area of rectangular sheet
4224 = b × l
4224 = 33 × l
l = 4224/33 = 128 cm
Hence, the length of the rectangular sheet is 128 cm.
Perimeter of rectangular sheet = 2(l+b)
= 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 1 m.
Diameter of road roller (d) = 84 cm
So, radius of road roller (r) = 84/2 = 42 cm [r = d/2]
Length of road roller (h) = 1 m = 100 cm
Curved surface area of road roller = 2πrh
= 26400 cm2
Area covered by road roller in 750 revolutions = 26400×750cm2
= 1980 m2 [1 m2= 10,000 cm2]
Hence, the area of the road is 1980 m2.
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 figure). If the label is placed 2 cm from top and bottom, what is the area of the label?
Diameter of cylindrical container (d) = 14 cm
So, radius of cylindrical container (r) = 14/2 = 7 cm [r = d/2]
Height of cylindrical container (H) = 20 cm
According to the figure,
Height of the label, say (h) = 20–2–2 ()
= 16 cm
Curved surface area of label = 2πrh
Hence, the area of the label is 704 cm2.