# SOLVING WORD PROBLEMS WITH CUBOID

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) sq. units

Surface Area  =  2(lw + wh + hl) sq.units

Problem 1 :

Find the total surface area and the lateral surface area of a cuboid whose length is 20 cm, width is 15 cm and height is 8 cm.

Solution :

Total surface area is

=  2(lw + wh + hl)

Substitute.

=  2[20(15) + 15(8) + 8(20)]

=  2 [300 + 120 + 160]

=  2(580)

=  1160 cm2

Lateral surface area is

=  2h(l + w)

Substitute.

=  2(8)(20 + 15)

=  16(35)

=  560 cm2

Problem 2 :

The dimensions of a cuboidal box are 6 m × 400 cm × 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 m2

Cost of painting the surface is \$22 per m2.

So, the required cost is

=  78(22)

=  \$1716

Problem 3 :

The dimensions of a hall is 10 m × 9 m × 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 m2

Cost of white washing is \$8.50 per m2.

So, the required cost is

=  394(8.50)

=  \$3349

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