SOLVING MENSURATION WORD PROBLEMS WITH THE SHAPE CUBOID

Practice Problems

Problem 1 :

Find the volume of a cuboid whose dimensions are

(i) length = 12 cm, breadth = 8 cm, height = 6 cm

(ii) length = 60 m, breadth = 25 m, height = 1.5 m

Solution :

(i) length = 12 cm, breadth = 8 cm, height = 6 cm

Volume of cuboid  =  l b h

  =  12 (8) (6)

  =  12 (48)

=  576 cm³

(ii) length = 60 m, breadth = 25 m, height = 1.5 m

Volume of cuboid  =  l b h

  =  60 (25) (1.5)

  =  60 (37.5)

=  2250 cm³

Problem 2 :

The dimensions of a match box are 6 cm × 3.5 cm × 2.5 cm. Find the volume of a packet containing 12 such match boxes.

Solution :

length  =  6 cm, breadth  =  3.5 cm and height  =  2.5 cm  

Volume of cuboid  =  lbh

  =  6 (3.5) (2.5)

  =  52.5 cm³

Volume of 12 boxes  =  52.5 (12)

  =  630 cm³

Problem 3 :

The length, breadth and height of a chocolate box are in the ratio 5 : 4 : 3. If its volume is 7500 cm³, then find its dimensions.

Solution :

Volume of box  =  7500 cm³

Let 5x, 4x and 3x be the length breadth and height of chocolate boxes respectively.

5x (4x) (3x)  =  7500

60x³  =  7500

x³  =  125

x  =  5 cm

length  =  5(5)  =  25 cm

breadth  =  4(5)  =  20 cm

height   =  3(5)  =  15 cm

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