Formulas given below can be used to find volume, lateral surface area and total surface of a cuboid.
Volume = l x w x h cubic units
Lateral surface area = 2h(l + w) square units
Total surface area = 2(lw + wh + hl) squareunits
Problem 1 :
Find the total surface area and lateral surface area of a cuboid whose length is 20 cm, width is 15 cm and height is 8 cm.
Solution :
Total surface area :
= 2(lw + wh + hl)
Substitute.
= 2[20(15) + 15(8) + 8(20)]
= 2 [300 + 120 + 160]
= 2(580)
= 1160 cm^{2}
Lateral surface area :
= 2h(l + w)
Substitute.
= 2(8)(20 + 15)
= 16(35)
= 560 cm^{2}
Problem 2 :
The dimensions of a cuboidal box are 6 m x 400 cm x 1.5 m. Find the cost of painting its entire outer surface at the rate of $22 per square meter.
Solution :
From the given information,
length (l) = 6 m
width (w) = 400 cm = 400/100 m = 4 m
height = 1.5 m
Outer surface area has six sides.
Then, the required area is
= 2(lw + wh + hl)
Substitute.
= 2[6(4) + 4(1.5) + 1.5(6)]
= 2[24 + 6 + 9]
= 2[39]
= 78 m^{2}
Cost of painting the surface is $22 per m^{2}.
So, the required cost is
= 78(22)
= $1716
Problem 3 :
The dimensions of a hall is 10 m x 9 m x 8 m. Find the cost of white washing the walls and ceiling at the rate of $8.50 per square meter.
Solution :
From the given information,
length (l) = 10 m
width (w) = 9 m
height = 8 m
Area of white washing is
= 2h(l + w) + lw
Substitute.
= 2(8)(10 + 9) + 10(9)
= 16(19) + 90
= 304 + 90
= 394 m^{2}
Cost of white washing is $8.50 per m^{2}.
So, the required cost is
= 394(8.50)
= $3349
Problem 3 :
The dimensions of a hall is 10 m x 9 m x 8 m. Find the cost of white washing the walls and ceiling at the rate of $8.50 per square meter.
Solution :
From the given information,
length (l) = 10 m
width (w) = 9 m
height = 8 m
Area of white washing is
= 2h(l + w) + lw
Substitute.
= 2(8)(10 + 9) + 10(9)
= 16(19) + 90
= 304 + 90
= 394 m^{2}
Cost of white washing is $8.50 per m^{2}.
So, the required cost is
= 394(8.50)
= $3349
Problem 4 :
The length, width and depth of a pond are 20.5 m, 16 m and 8 m respectively. Find the capacity of the pond in liters.
Solution :
l = 20.5 m, w = 16 m, h = 8 m
Capacity of pond :
= lx w x h
= 20.5(16)(8)
= 2624 m^{3}
1 m^{3} = 1000 liters,
= 2624(1000) liters
= 2624000 liters
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