A right cylinder has a radius of 3 and a height of 12. What is its surface area?

A. [tex]$72 \pi$[/tex] units [tex]$^2$[/tex]

B. [tex]$45 \pi$[/tex] units [tex]$^2$[/tex]

C. [tex]$90 \pi$[/tex] units [tex]$^2$[/tex]

D. [tex]$108 \pi$[/tex] units [tex]$^2$[/tex]



Answer :

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]