Question

Find the curved surface area of a cylinder given below:

Answer 1

Hint: Observe the basic structure of the given figure and deduce the area . Remember 12 m is the diameter of the base of the cylinder.

Complete step by step answer:
A cylinder is a three dimensional object with one curved side and two round flat bases. The two round surfaces are identical .
After observing the cylinder carefully, we see that a cylinder is actually made up of three faces.The two circles forming the base and the top of the cylinder. Both these circles are of the same size, which means they have the same radius. The curved surface of the cylinder is formed from a rectangle . Fold the rectangle either lengthwise or widthwise to form a curved surface.
The area of the circle of the cylinder is $\pi {{r}^{2}}$where $r$is the radius of the circle.
As there are two circles of same area, area of two circles, the top and the base is $2\pi {{r}^{2}}$
The radius $r$of a cylinder is the radius of its base circle.
Now moving on to the rectangle:
Area of rectangle=length × breadth
If the rectangle is folded Breadth wise, then the length of the rectangle is equal to the height of the cylinder that is $h$.
The breadth of the rectangle is equal to the circumference of the circle which is $2\pi r$
So the area of the rectangle is $2\pi r\times h$=$2\pi rh$
So the area of the cylinder is : $2\pi {{r}^{2}}+2\pi rh$
This is also known as the total surface area of the cylinder.
Total surface area of cylinder=$2\pi r(r+h)$
Where r is the radius of the base of the cylinder and h is the height of the cylinder.
The curved surface area of the cylinder is equal to the area of the curved surface formed by the rectangle which is equal to $2\pi rh$.
Now, height $h=40m$and diameter $d=12m$is given in the cylinder.
$r=\dfrac{d}{2}=\dfrac{12}{2}=6$
Applying the formula,we get
$2\pi rh=2\times \pi \times 6\times 40=1507.2$${{m}^{2}}$

Note: Always take care of the units of the dimensions, most of the mistakes are made with the units. Note that the total surface area of the cylinder and curved surface area of the cylinder are different.