Page 241 - ICSE Math 8

Surface area of a cube

The six faces of a cube are squares of the same size, i.e., l = b = h = a (edges of cube).
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\ Surface area of a cube = 2(a × a + a × a + a × a) sq. units = 2(a + a + a ) sq. units
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= 2(3a ) sq. units = 6a sq. units = 6(side) sq. units
Length of the diagonal of a cube = 3a units = 3 (edge) units
Lateral surface area of a cube = 2 × a(a + a) sq. units = 2a(2a) sq. units
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= 4a sq. units = 4(edge) sq. units
Example 9: Find the total surface area (TSA), lateral surface area (LSA) and length of the diagonal of a
cuboid of dimensions 10 cm × 0.8 dm × 5 cm.
Solution: Length (l) = 10 cm, breadth (b) = 0.8 dm = (0.8 × 10) cm = 8 cm and height (h) = 5 cm
TSA = 2(lb + bh + hl) = 2(10 × 8 + 8 × 5 + 5 × 10) cm 2

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= 2(80 + 40 + 50) cm = (2 × 170) cm = 340 cm 2
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LSA = 2h(l + b) = 2 × 5 × (10 + 8) cm = 10 × 18 = 180 cm 2
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10 + ()
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Length of diagonal = l + b 2 + h 2 = () 2 8 + () 2 = 100 64 25+ + = 189
= 321 cm or 13.75 cm (approx.)
Example 10: Find the lateral surface area and the length of diagonal of a cube of edge 8 cm.
Solution: Edge of the cube = 8 cm
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LSA = 4 × (Edge) = 4 × (8) cm = (4 × 64) cm = 256 cm 2
Diagonal of cube = 3 × Edge = 3 × 8 cm = 8 3 cm
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Example 11: Find the total surface area of a cube whose volume is 729 cm .
Solution: Volume of cube = 729 cm 3
Let the edge of the cube be x cm.
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Then, x = 729 fi x = 729 = 9 cm { Volume = (edge) }
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TSA of cube = 6 (edge) = 6x = 6 × (9) cm = (6 × 81) cm = 486 cm 2
Example 12: A room is 12 m long, 6 m broad and 3 m high. It has 2 doors each measuring 2.5 m × 1.5 m
and 4 windows each measuring 1.5 m × 1.5 m. Find the cost of whitewashing its walls and
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roof at the rate of ` 6 per m .
Solution: Length of room (l) = 12 m, Breadth of room (b) = 6 m, Height of room (h) = 3 m
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Area of 4 walls = 2h (l + b) = 2 × 3 × (12 + 6) m = 2 × 3 × 18 = 108 m 2
Area of roof = l × b = 12 m × 6 m = 72 m 2
Area of 1 door = 2.5 m × 1.5 m = 3.75 m 2
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\ Area of 2 doors = (2 × 3.75) m = 7.5 m 2
Area of 1 window = 1.5 m × 1.5 m = 2.25 m 2
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\ Area of 4 windows = (4 × 2.25) m = 9 m 2
Area to be whitewashed = Area of 4 walls + Area of roof – Area of 2 doors – Area of 4 windows
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= (108 + 72 – 7.5 – 9) m = 163.5 m 2
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Cost of whitewashing 1 m area = ` 6
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\ Cost of whitewashing 163.5 m area = ` (6 × 163.5) = ` 981

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