Page 179 - Maths Skills - 8

Mensuration 177

Example 2: Find the total surface and lateral surface area of a cuboid whose length, breadth and height are
3 m, 2.5 m and 1.5 m respectively.
Solution: Given: l = 3 m, b = 2.5 m and h = 1.5 m
Total surface area of a cuboid = 2(lb + bh + hl)
= 2(3 × 2.5 + 2.5 × 1.5 + 1.5 × 3) m 2

= 2(7.5 + 3.75 + 4.5) m = 2(15.75) m = 31.5 m 2
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Lateral surface area of a cuboid
= 2 (l + b)h = 2(3 + 2.5) × 1.5 = 16.5 m .
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Example 3: Find the cost of polishing a cuboid at ` 2.50 per sq. m whose length, breadth and height are 4 m,
3.5 m and 3 m respectively.

Solution: Given: l = 4 m, b = 3.5 m and h = 3 m.
Total surface area of the cuboid = 2(lb + bh + hl)
= 2(4 × 3.5 + 3.5 × 3 + 3 × 4) = 2(14 + 10.5 + 12) = 73 sq. m
So, cost of polishing the cuboid = 73 × 2.5 = ` 182.50.

Example 4: Find the area of the four walls of a room whose length, breadth and height are 7 m, 5 m and 4 m
respectively. Also, find the cost of whitewashing the walls, if the rate of whitewashing is ` 6 per
m . (Ignore the doors, windows and other openings.)
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Solution: Given: l = 7 m, b = 5 m and h = 4 m.
Area of the four walls of a room = 2(l + b) h
= 2(7 m + 5 m) 4 m = 2 × 12 m × 4 m = 96 m 2

Cost of whitewashing = ` 6 × 96 = ` 576.

Example 5: Two cubes each of 4 cm edge length are joined end to end to form a cuboid. Find the total surface
area and the lateral surface area of the cuboid so formed.
Solution: When two cubes are joined, a cuboid is obtained.
Length of cuboid (l) = 4 cm + 4 cm = 8 cm

Breadth of cuboid (b) = 4 cm
Height of cuboid (h) = 4 cm

Total surface area of cuboid = 2(lb + bh + hl)
= 2 (8 × 4 + 4 × 4 + 4 × 8) cm 2

= 2(32 + 16 + 32) cm = 2 × 80 = 160 cm 2
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Lateral surface area of cuboid = 2h(l + b)
= 2 × 4 × (8 + 4) cm = (8 × 12) cm = 96 cm 2
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Exercise 11.2

1. Find the total surface area and the lateral surface area of the cubes whose edges are.

(i) 13 cm (ii) 7 m (iii) 2 m 25 cm (iv) 11 m