Question

What is the surface area of a cylinder that has top and bottom if the height is 8.5 units and the diameter is 3 units?
A. \[18\pi \,\text{square}\,\text{units}\]
B. \[30\pi \,\text{square}\,\text{units}\]
C. \[32\pi \,\text{square}\,\text{units}\]
D. \[36\pi \,\text{square}\,\text{units}\]

Answer 1

Hint: We will substitute the given diameter from that we have to find the radius from \[d=2r\] and also given the height in the formula of surface area of a cylinder. The formula is \[S=2\pi r(r+h)\] where \[S\] is the surface area, \[r\] is the base radius and \[h\] is the height of the cylinder. From this equation we will find the Surface area of the cylinder.

Complete step by step answer:
Diameter of the circle is given as 3 units and Height of the Cylinder is 8.5 units. The figure will be as follows:

Diameter is given in the question that is 3 units and height is 8.5 units
To find the radius formula is given by \[d=2r\]
As we known that \[d=3\,\] substitute in this formula we get:
\[r=\dfrac{3\,}{2}=1.5\] units.
Formula for surface area of a circle is given by
\[S=2\pi r(r+h)\]
Here we have to find the surface area of the cylinder and substitute the value of radius and height we get:
\[S=2\pi \times 1.5(1.5+8.5)\]
By simplifying this we get:
\[S=2\pi \times 1.5(10)\]
By further solving this we get:
\[S=30\pi \] square units.
Therefore, the surface area of the cylinder is \[S=30\pi \] square units.

Therefore, the correct answer is “option B”.

Note: A cylinder is a three-dimensional solid shape having two parallel circular bases joined by a curved surface at a fixed distance. It can also be seen as a set of circular discs stacked on another. You have also noted some examples regarding cylinders that are candles, water tank pipes, wells etc. Most of the students say that they will substitute the diameter instead of radius in the Formula of surface area. That is wrong because we know that diameter is equal to twice the radius. From that you will get the value of radius then substitute the formula to get the value of surface area of the cylinder.