Hi

MY question is if a cylinder has a volume of 72cm cubed and a cross-sectional area of 18cm squared. Work out the height of the cylinder

Can someone show me how we do it by the steps

The cross-section of a cylinder is a circle.
so pi(r)^2=18

solve for r

let the height be h cm

volume of cylinder = pi(r^2)h

72 = pi(r^2)h, but you know r, so you can now find h

To find the height of the cylinder, we need to use the given information about the volume and cross-sectional area.

Step 1: Determine the radius of the cylinder.
The cross-sectional area of the cylinder is given as 18 cm², and we know that the cross-section is a circle. The formula for the area of a circle is A = πr², where A is the area and r is the radius. So, we have:
πr² = 18

To solve for r, divide both sides of the equation by π:
r² = 18/π

Step 2: Calculate the radius.
Take the square root of both sides to find the value of r:
r = √(18/π)

Step 3: Find the height of the cylinder.
The volume of a cylinder is calculated as V = πr²h, where V is the volume and h is the height. We are given that the volume of the cylinder is 72 cm³, so we have:
72 = π(√(18/π))²h

Simplify the equation:
72 = 18h/π

To solve for h, multiply both sides of the equation by π and then divide by 18:
h = 72π/18

Simplify the fraction:
h = 4π

So, the height of the cylinder is 4π cm, where π is approximately equal to 3.14.