Question

b) The rectangular tank of length, breadth and height are 12cm, 10cm and 6cm
respectively is full of water. If this water is poured into a smaller tank. How
many tanks of length 5cm, breadth 4cm and height 3cm are required ?​

Answer 1

Answer:

12 Tanks

Step-by-step explanation:

Given,

Of greater tank,

length = 12cm, breadth = 10cm, height = 6cm.

Of smaller tank,

length = 5cm, breadth = 4cm, height = 3cm

volume of a cuboid = length × breadth × height

So,

• volume of greater tank = 12 × 10 × 6

= 720cm cube

• volume of smaller tank = 5 × 4 × 3

= 60cm cube

Therefore,

Number of tanks required to gain volume of greater tank = volume of greater tank / volume of

smaller tank

= 720 / 60

= 12

So,

12 tanks will be required to gain the same volume of greater tank

Answer 2

$\bf{\underline{Given}}$

Dimensions of bigger tank

• Length = 12 cm
• Breadth = 10 cm
• Height = 6 cm

Dimensions of smaller tank

• Length = 5 cm
• Breadth = 4 cm
• Height = 3 cm

$\bf{\underline{To\:Find}}$

Number of small tanks required to store the water from bigger tank.

$\bf{\underline{Solution}}$

Dimensions of bigger tank:-

Length = 12 cm

Breadth = 10 cm

Height = 6 cm

$\sf{Volume\:of\:bigger\:tank\:(V_1) = 12\times10\times6\:\:cm^3}$

= $\sf{V_1 = 120\times 6\:\:cm^3}$

= $\sf{V_1 = 720\:\:cm^3}$

Now,

Dimensions of smaller tank:-

Length = 5 cm

Breadth = 4 cm

Height = 3 cm

$\sf{Volume\:of\:smaller\:tank \:(V_2) = 5\times4\times3\:\:cm^3}$

= $\sf{V_2 = 20\times 3}$

= $\sf{V_2 = 60}$

Now,

$\sf{Number\: of\: tanks\: required = \dfrac{V_1}{V_2}}$

= $\sf{Number\:of\:tanks\:required = \dfrac{720}{60}}$

= $\sf{Number\:of\:small\:tanks\:required = 12}$

$\sf{\therefore}$ 12 small tanks will be required to store the water of bigger tank.

$\bf{\underline{Additional\:Information}}$

• $\sf{Volume\:of\:cuboid=(Length\times Breadth\times Height)\:sq.units}$

• $\sf{TSA\:of\:cuboid = 2(Length\times Breadth + Breadth\times Height + Height\times Length)\:sq.units}$

• $\sf{LSA\:of\:cuboid = [2(Length + Breadth)\times Height]\:\:sq.units}$

$\bf{\underline{Note}}$

TSA stands for Total Surface Area.

LSA stands for Lateral Surface Area.