Answer:
[tex]\boxed{\text{1172 in}^{2}}[/tex]
Step-by-step explanation:
SA = SA(prism) + SA(cylinder) – 2SA(cylinder base)
1. Surface area of rectangular prism
The formula for the surface area of a rectangular prism is
S = 2(lw + lh + wh)
Data:
l = 16 in
w = 11 in
h = 11 in
Calculations:
2(Top + Bottom) = 2lw = 2 × 16 × 11 = 352 in²
2(Front + Back) = 2lh = 2 × 16 × 11 = 352 in²
2(Left + Right) = 2wh = 2 × 11 × 11 = 242 in²
Total area = 946 in²
2. Surface area of cylinder
A = A(top) + A (base) + A(side) = 2A(base) + A(side)
Data:
d = 8 in
h = 9 in
Calculations:
r = ½d = ½ × 8 = 4 in
[tex]\begin{array}{rcl}SA & = & 2\pi r^{2}+ 2\pi rh \\& = & 2 \times 3. 14\times 4^{2} +2\times 3. 14 \times 4\times 9\\& = & 6.28\times 16 + 226.08\\& = & 100.48 + 226.08\\& = & 326.56 \text{ in}^{2}\\\end{array}[/tex]
3. Excluded area
Excluded area = 2A(base) = 100.48 in²
4. Total area
[tex]A = 946 + 326.56 - 100.48 \approx \boxed{\textbf{1172 in}^{2}}[/tex]
