To find the surface area of a cylinder, we use the formula:
\[ \text{Surface Area} = 2\pi r(h + r) \]
where:
- \( r \) is the radius of the cylinder,
- \( h \) is the height of the cylinder.
Given that the diameter of the cylinder is 7, the radius \( r \) is half of that:
\[ r = \frac{7}{2} = 3.5 \]
The height \( h \) is given as 8.
Now, substitute the values into the formula:
\[ \text{Surface Area} = 2 \times 3.14 \times 3.5 \times (8 + 3.5) \]
Calculate \( h + r \):
\[ h + r = 8 + 3.5 = 11.5 \]
Now substitute this back into the formula:
\[ \text{Surface Area} = 2 \times 3.14 \times 3.5 \times 11.5 \]
Calculate it step by step:
- Calculate \( 2 \times 3.14 = 6.28 \)
- Calculate \( 3.5 \times 11.5 = 40.25 \)
- Finally calculate \( 6.28 \times 40.25 \)
\[ 6.28 \times 40.25 \approx 252.77 \]
Thus, the surface area of the cylinder is approximately:
252.77 square yards.
11 answers