To find the surface area of a right cylinder, you can use the formula for the surface area of a cylinder, which combines the area of the two circular bases and the area of the rectangular side that wraps around the cylinder.
The surface area [tex]\( A \)[/tex] of a right cylinder with radius [tex]\( r \)[/tex] and height [tex]\( h \)[/tex] is given by:
[tex]\[ A = 2 \pi r h + 2 \pi r^2 \][/tex]
Let's break this down step-by-step for a cylinder with a radius [tex]\( r = 5 \)[/tex] units and height [tex]\( h = 9 \)[/tex] units:
1. Calculate the area of the two circular bases:
- The area of one circular base is [tex]\( \pi r^2 \)[/tex].
- Since there are two bases, the total area for the bases is [tex]\( 2 \pi r^2 \)[/tex].
Thus:
[tex]\[ 2 \pi r^2 = 2 \pi (5)^2 = 2 \pi \cdot 25 = 50 \pi \][/tex]
2. Calculate the area of the side (the lateral surface area):
- The lateral surface area is given by the circumference of the base times the height of the cylinder.
- The circumference of the base is [tex]\( 2 \pi r \)[/tex], and multiplying this by the height [tex]\( h \)[/tex] gives the lateral surface area.
Thus:
[tex]\[ 2 \pi r h = 2 \pi \cdot 5 \cdot 9 = 90 \pi \][/tex]
3. Add the areas together to find the total surface area:
- We now add the areas of the bases and the lateral surface area.
Thus:
[tex]\[ A = 2 \pi r h + 2 \pi r^2 = 90 \pi + 50 \pi = 140 \pi \][/tex]
Therefore, the surface area of the right cylinder is [tex]\( 140 \pi \)[/tex] square units.
The correct answer is:
[tex]\[ B. 140 \pi \text{ units}^2 \][/tex]
