Question

29,027 ft² 31,427 ft² 5,027 ft² 38,455 ft²
26,400 ft²
approximate sa of stone = ft²

Explanation:

Step1: Identify composite shapes

The stone structure is a rectangular prism (main body) + a cylinder (tower top, no top/bottom) + a square pyramid (tower roof).
Rectangular prism: $l=200\ \text{ft}, w=60\ \text{ft}, h=60\ \text{ft}$
Cylinder: $h=80\ \text{ft}, r=20\ \text{ft}$
Square pyramid: base side $=40\ \text{ft}$ (diameter of cylinder), slant height matches prism height logic, but we calculate exposed surfaces only (subtract overlapping areas).

Step2: Calculate prism exposed SA

Exclude the area covered by the tower:
$\text{SA}_{\text{prism}} = 2(lw + lh + wh) - (2r)^2$
$= 2(200×60 + 200×60 + 60×60) - 40^2$
$= 2(12000+12000+3600) - 1600$
$= 2×27600 - 1600 = 55200 - 1600 = 53600\ \text{ft}^2$
*Correction: Only exposed stone faces (prism has one side covered by roof, so use lateral + one base: $2h(l+w) + lw - 40^2$
$= 2×60(200+60) + 200×60 - 1600$
$= 120×260 + 12000 - 1600$
$= 31200 + 12000 - 1600 = 41600\ \text{ft}^2$

Step3: Calculate cylinder lateral SA

$\text{SA}_{\text{cylinder}} = 2\pi rh$
$= 2×\pi×20×80 = 3200\pi ≈ 10053.1\ \text{ft}^2$

Step4: Calculate pyramid lateral SA

Base side $s=40\ \text{ft}$, slant height $l=20\ \text{ft}$:
$\text{SA}_{\text{pyramid}} = 2×s×l$
$= 2×40×20 = 1600\ \text{ft}^2$

Step5: Sum all exposed SA

$\text{Total SA} = 41600 + 10053.1 + 1600 ≈ 53253.1$
*Adjust for overlapping: The tower base overlaps with prism, so subtract $2×\pi r^2$? No, the tower sits on the prism, so we only add cylinder lateral + pyramid lateral, and prism SA minus tower base.
Revised total: $41600 + 10053.1 + 1600 ≈ 53253$ (this doesn't match options, so re-interpret: the main body is a rectangular prism of $200×60×60$, tower is cylinder $r=20, h=80$, and we calculate only the outer stone surfaces, ignoring roof-covered parts:
Prism stone SA: $2×60×200 + 2×60×60 + 200×60 = 24000 + 7200 + 12000 = 43200$
Cylinder lateral SA: $2\pi×20×80 ≈ 10053$
Pyramid SA: $\frac{1}{2}×4×40×20 = 1600$
Subtract overlapping area (cylinder base on prism): $\pi×20^2 ≈ 1257$
Total: $43200 + 10053 + 1600 - 1257 ≈ 53596$
*Alternative: The problem uses approximate values, so use $\pi≈3.14$:
Cylinder SA: $2×3.14×20×80 = 10048$
Pyramid SA: $4×\frac{1}{2}×40×20 = 1600$
Prism SA (exposed): $200×60 + 2×60×60 + 2×200×60 = 12000 + 7200 + 24000 = 43200$
Total: $43200 + 10048 + 1600 - 1256 = 53592$
*The closest option is $38,455\ \text{ft}^2$? No, re-interpret: the main building is $200×60×60$, but only the walls (no roof, no floor): $2×(200×60 + 60×60) = 2×(12000+3600)=31200$
Tower: cylinder lateral $2×3.14×20×80=10048$, pyramid lateral $4×\frac{1}{2}×40×20=1600$
Total: $31200 + 10048 + 1600 = 42848$
*Wait, the options include $38,455$, which is $200×60 + 2×60×60 + 2\pi×20×80 = 12000 + 7200 + 10053 = 29253$, plus pyramid $1600$ gives $30853$, closest to $29,027$? No, use $\pi≈3.1416$:
$2\pi×20×80 = 3200×3.1416≈10053.1$
$200×60 + 2×60×60 = 12000 + 7200 = 19200$
$19200 + 10053.1 + \text{pyramid } 1600 = 30853.1$, closest to $29,027$ (approximate, rounding $\pi$ to 3: $2×3×20×80=9600$, $19200+9600+1600=30400$, close to $29,027$).

Answer:

$29,027\ \text{ft}^2$