Question

Volume of a conical water tank is 864 cubic meter. If the diameter of the base is 14 m, what will its height be?

Answer 1

Given :-  

• Volume of a conical water tank is 864 cubic meter.  

• If the diameter of the base is 14 m

To Find :-  

• what will its height be?

Solution :-  

~Here, we’re given the volume of a conical tank and it’s diameter. From the given diameter we can find the radius and then the height of the conical tank by applying the formula of volume of a cone.  

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As we know that ,  

$\sf \bigstar \;\; Radius = \dfrac{Diameter}{2}$  

$\sf \bigstar \;\; Volume\;of\;cone = \dfrac{1}{3} \times ( \pi r^{2} h )$  

Where,  

• h is height  
• r is radius  

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Finding the Radius :-  

$\sf \implies \dfrac{14}{2}$

$\sf \leadsto 7\; m$ 

Finding the height :-  

$\sf \implies 864\;m^{3} = \dfrac{1}{3} \times \dfrac{22}{7} \times 7 \times 7 \times h$ 

$\sf \implies 864 = \dfrac{154}{3} \times h$

 

$\sf \implies h = 864 \times \dfrac{3}{154}$

 $\sf \leadsto h = 16.83 \; m$

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Hence,

• Height of the conical tank is 16.83 m  

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