Question

20p!!!ill mark you as brain please help!!! hurry

Answer 1

Answer:

$\boxed{\text{1172 in}^{2}}$

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

$\begin{array}{rcl}SA & = & 2\pi r^{2}+ 2\pi rh \\& = & 2 \times 3. 14\times 4^{2} +2\times 3. 14 \times 4\times 9\\& = & 6.28\times 16 + 226.08\\& = & 100.48 + 226.08\\& = & 326.56 \text{ in}^{2}\\\end{array}$

3. Excluded area

Excluded area = 2A(base) = 100.48 in²

4. Total area  

$A = 946 + 326.56 - 100.48 \approx \boxed{\textbf{1172 in}^{2}}$