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

r =
`\sqrt{(v)/(\pi h) }`

27.2cm

Step-by-step 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

`(v)/(\pi h)` =
`(\pi r^(2)h )/(\pi h )`

r² =
`(v)/(\pi h)`

r =
`\sqrt{(v)/(\pi h) }`

ii.

Radius of the water tank;

r =
`\sqrt{(15000000)/(\pi x 6461.76) }` = 27.2cm