Question

This right cylindrical tank can hold 96π cubic meters of sand. The height of the cylindrical tank is 6 meters. Find the length, in meters, of r, the radius of the base of the tank.

Answer 1

4 meters

Explanation:

Given:

• Height of cylinderical tank: 6 meters
• Volume of cylinderical tank: 96π meters³

⇒ Volume of cylinder: πr²h

Substituting the height and the volume in the formula:

⇒ Volume of cylinder: πr²h

⇒ 96π meters³ = (π)(r²)(6)

Dividing both sides by 6π to isolate "r" (Radius):

⇒ 96π/6π = (π)(r²)(6)/6π

⇒ 96π/6π = (r²)

⇒ 96/6 = (r²)

⇒ 16 = (r²)

Taking a square root both sides:

⇒ √16 = √(r²)

⇒ √4 x 4 = √(r x r)

⇒ 4 meters = r

The measure of the radius is 4 meters.

Answer 2

4 m

Explanation:

The formula for the volume of a cylinder is πr^2 x h

r = radius h = height

So, with this you can reverse it to find the radius since you know the height.

96π/6 = 16π

√16π = 4π

radius = 4 m