Page 288 - Start Up Mathematics_8 (Non CCE)

Total Surface Area (TSA) of the cuboid
= Sum of the areas of its six faces
= 2 ( lb) + 2(bh) + 2(hl) = 2(lb + bh + hl) cm 2

2
2
2
Length of the diagonal (AE) = l + b + h cm
Now consider a room of length (l), breadth (b) and height (h). A room is also a cuboid. So, the surface
area of the four walls [also called the lateral surface area (LSA)] = 2(lh) +2(bh)
\ LSA = 2h(l + b) sq. units = 2 × height × (length + breadth) sq. units
= Perimeter × Height sq. units
(b) 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).
2
2
2
\ Surface area of a cube = 2(a × a + a × a + a × a) sq. units = 2(a + a + a ) sq. units
2
2
2
= 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
2
2
= 4a sq. units = 4(edge) sq. units
Example 15: 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
2
2
= 2(80 + 40 + 50) cm = (2 × 170) cm = 340 cm 2
2
LSA = 2h(l + b) = 2 × 5 × (10 + 8) cm = 10 × 18 = 180 cm 2
2
2
10 + ()
Length of diagonal = l + b 2 + h 2 = () 2 8 + () 2 = 100 64 25+ + = 189
5
= 321 cm or 13.75 cm (approx.)
Example 16: Find the lateral surface area and the length of diagonal of a cube of edge 8 cm.
Solution: Edge of the cube = 8 cm
2
2
2
2
LSA = 4 × (Edge) = 4 × (8) cm = (4 × 64) cm = 256 cm 2
Diagonal of cube = 3 × Edge = 3 × 8 cm = 8 3 cm
3
Example 17: 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.
3
3
then x = 729 { Volume = (Edge) }
3
fi x = 729 = 9 cm
2
2
2
2
2
TSA of cube = 6 (edge) = 6x = 6 × (9) cm = (6 × 81) cm = 486 cm 2
Example 18: 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
2
roof at the rate of ` 6/m .
Solution: Length of room (l) = 12 m, Breadth of room (b) = 6 m, Height of room (h) = 3 m
2
Area of 4 walls = 2h (l + b) = 2 × 3 × (12 + 6) m = 2 × 3 × 18 = 108 m 2
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