Question

PLEASE HELP ASAPPP


A cylinder shaped water tank has a height of 212 ft (6461.76 cm), and is able
to hold 15,000 gallons of water (15,000,000 mL or 15,000,000 cm3). The
volume of a cylinder is expressed by the equation
V = tr^2h
Where V is the volume, r is the radius, and h is the height of the cylinder.
Express the radius (r) in terms of volume (V) and height (h), then determine
the radius of a cylinder water tank (in centimeters) that is filled to capacity.

Answer 1

Answer:

 r =  $\sqrt{\frac{v}{\pi h} }$

27.2cm

Explanation:

Given parameters:

Height of tank  = 6461.76cm

Volume of water  = 15000000cm³

Volume of cylinder  = $\pi$ r² h

 

i. Express radius in terms of volume;

  we are to make radius the subject of the expression;

              v = $\pi$ r² h  

     divide both sides by πh

         $\frac{v}{\pi h}$   = $\frac{\pi r^{2}h }{\pi h }$  

              r²   =  $\frac{v}{\pi h}$

              r =  $\sqrt{\frac{v}{\pi h} }$

ii.

Radius of the water tank;

             r  = $\sqrt{\frac{15000000}{\pi x 6461.76} }$   = 27.2cm