Question

An iron tank of length 5 m and width 4 m and contains 50 m^3 of water. A small model tank is made and its volume is 400 m^3. Find the height of the model.

Answer 1

l=h=5m

w=r=4m

v=50m^3

v of small tank=400m^3

h=pie r^2 h

h= pie 2×2×h

h=22/7×2×2×h

88/7×h

h=12.57 m

Answer 2

The height of model is 5 m.

Explanation:

Given : An iron tank of length 5 m and width 4 m and contains 50 $m^3$ of water.

Since , volume of rectangular prism : $V=\text{length x width x height}$

i.e.

$50=5\times4\times\text{height}\\\\\Rightarrow\text{height}=\dfrac{50}{20}=2.5\ m$

Also, similar modal has proportional dimensions , thus

Dimension of small model tank:

Length  = 5 k  , where k is the scale factor

Width  = 4 k

Height = 2.5k

Volume = $5k\times4k\times2.5k=50k^3$

Since volume of small model tank is 400 m³.

i.e.

$50k^3=400\Rightarrow\ k^3=\dfrac{400}{50}=8\\\\\rightarrow\ k=\sqrt[3]{8} =2$

Then , the height of model = 2.5 (2) = 5 m

Hence, the height of model is 5 m.

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