Find the lateral area in square metres of a steam pipe that is 15 cm in diameter and 3 m long.

To find the lateral area of a cylindrical steam pipe, you use the formula for the lateral surface area of a cylinder, which is given by:

[ \text{Lateral Area} = 2\pi r h ]

where ( r ) is the radius of the cylinder and ( h ) is the height (or length) of the cylinder.

In this scenario, the diameter of the steam pipe is 15 cm, so the radius ( r ) is half of that:

[ r = \frac{15 , \text{cm}}{2} = 7.5 , \text{cm} = 0.075 , \text{m} ] (since we convert centimeters to meters for consistency in units).

The length of the steam pipe ( h ) is given as 3 m.

Now, substituting the values into the formula:

[

\text{Lateral Area} = 2\pi (0.075 , \text{m})(3 , \text{m})

]

Calculating this step-by-step:

1. Calculate ( 2\pi(0.075)(3) ):

• First, ( 2 \