Question

Find the height (in meters) of a storage tank in the shape of a right circular cylinder that has a circumference measuring 4 m and a volume measuring 36 m3.

Answer 1

9π m ≈ 28.27m

Explanation:

The volume of a right cylinder is given by the formula

πr²h where r is the radius of the base of the cylinder(which is a circle), h is the height of the cylinder

Circumference of base of cylinder is given by the formula 2πr

Given,

2πr = 4m

r = 2/π m

Volume given as 36 m³

So πr²h = 36
π (2/π)² h = 36

π x 4/π² h = 36

(4/π) h = 36

h = 36π/4 = 9π ≈ 28.27m

Answer 2

`h = \bf 28.3 \space\ m`

Explanation:

• We are given:

○ Volume = 36 m³,

○ Circumference = 4 m

• Let's find the radius of the cylinder first:

`\mathrm{Circumference} = 2 \pi r`

Solving for
`r` :

⇒
`4 = 2 \pi r`

⇒
`r = (4)/(2\pi)`

⇒
`r = \bf (2)/(\pi)`

• Now we can calculate the height using the formula for volume of a cylinder:

`\mathrm{Volume} = \boxed{\pi r^2 h}`

Solving for
`h` :

⇒
`36 = \pi \cdot ((2)/(\pi)) ^2 \cdot h`

⇒
`h = (36 \pi^2)/(4 \pi)`

⇒
`h = 9 \pi`

⇒
`h = \bf 28.3 \space\ m`