To find the surface area of a right cylinder, we use the formula for the surface area of a cylinder, which is:
[tex]\[ \text{Surface Area} = 2\pi r(h + r) \][/tex]
Here,
- [tex]\( r \)[/tex] is the radius of the cylinder,
- [tex]\( h \)[/tex] is the height of the cylinder,
- and [tex]\( \pi \)[/tex] is a constant approximately equal to 3.14159.
Given:
- The radius [tex]\( r \)[/tex] is 5 units,
- The height [tex]\( h \)[/tex] is 9 units.
We plug these values into the formula:
[tex]\[ \text{Surface Area} = 2\pi(5)(9 + 5) \][/tex]
First, calculate the expression inside the parentheses:
[tex]\[ 9 + 5 = 14 \][/tex]
Next, multiply by the radius:
[tex]\[ 2 \pi \times 5 \times 14 \][/tex]
Now multiply:
[tex]\[ 2 \times 5 = 10 \][/tex]
So the expression becomes:
[tex]\[ 10 \pi \times 14 \][/tex]
[tex]\[ 10 \times 14 = 140 \][/tex]
Thus the surface area is:
[tex]\[ 140 \pi \][/tex]
Finally, multiplying by [tex]\( \pi \)[/tex] (approximately 3.14159) gives:
[tex]\[ 140 \pi \approx 439.822971502571 \, \text{units}^2 \][/tex]
So, the surface area of the cylinder is approximately 439.822971502571 square units.
Out of the given options, none match the exact calculated value, thus indicating that the provided choices may be incorrect in relation to the calculated value.
