Question

Cartons of dimension 10 x cm 5x cm x 5 cm needs to be stacked in a truck of dimension, 2 x m 60 cm
* 40 cm. How many cartons can be stacked in the truck.​

Answer 1

⇒ Given:

Dimensions of the carton = 10cm x 5cm x 5cm

Dimensions of the truck = 2m x 60cm x 40cm

⇒ To Find:

The number of cartons that can be stacked in the truck.

⇒ Analysis:

In this question, we first need to find the volume of one carton and then the volume of the truck. Then we must divide the volume of one carton from the total volume of the truck. This will give us the number of cartons that can be stored in the truck.

⇒ Formulae to be used:

→ $\boxed{\sf{Volume\:of\:a\:cuboid=lbh}}$

→ $\boxed{\sf{1\:m=100\:cm}}$

⇒ Solution:

✳ Carton:

Length = 10 cm

Breadth = 5 cm

Height = 5 cm

Volume of one carton = length x breadth x height

= 10 x 5 x 5 cm

= 250 cm³

✳ Truck:

Length = 2 m = 200 cm

Breadth = 60 cm

Height = 40 cm

Volume of the truck = length x breadth x height

= 200 x 60 x 40

= 480000 cm³

✳ No. of cartons that can be stored in the truck:

$\sf{No.\:of\:cartons=\dfrac{Volume\:of\:truck}{Volume\:of\:one\:carton}}$

$\sf{No.\:of\:cartons=\dfrac{480000\:cm^3}{250\:cm^3}}$

$\sf{=1920\:cartons}$

Hence the no. of cartons that can be stored in the truck is 1920.

Cuboid:

  A cuboid is a three-dimensional figure with 6 rectangular faces, 12 edges and 8 vertices. Three important formulae related to the cuboid are:

→ LSA = 2 (lh + bh)

→ TSA = 2 (lh + bh + lb)

→ Volume = lbh