To calculate the surface area of a right cylinder, we use the formula for the surface area, which is given by:
[tex]\[ \text{Surface Area} = 2 \pi r (r + h) \][/tex]
where:
- \( \pi \) is a constant (approximately 3.14159)
- \( r \) is the radius of the cylinder
- \( h \) is the height of the cylinder
For this problem, we are given:
- Radius (\( r \)) = 3 units
- Height (\( h \)) = 12 units
Let's substitute these values into the formula:
[tex]\[ \text{Surface Area} = 2 \pi \times 3 \times (3 + 12) \][/tex]
First, we compute the inner sum:
[tex]\[ 3 + 12 = 15 \][/tex]
Then, we substitute back:
[tex]\[ \text{Surface Area} = 2 \pi \times 3 \times 15 \][/tex]
Now, we multiply these values:
[tex]\[ \text{Surface Area} = 2 \times 3 \times 15 \times \pi \][/tex]
[tex]\[ \text{Surface Area} = 90 \pi \, \text{units}^2 \][/tex]
Thus, the surface area of the right cylinder is:
[tex]\[ \boxed{90 \pi \, \text{units}^2} \][/tex]
So, the correct answer is:
C. [tex]\( 90 \pi \, \text{units}^2 \)[/tex]
