To find the surface area of the hourglass-shaped sculpture made of two cones, we first need to calculate the lateral surface area of one cone and then double that, since there are two identical cones.
The formula for the lateral surface area (\(A\)) of a cone is given by:
\[ A = \pi r l \]
where:
- \(r\) is the radius of the base of the cone,
- \(l\) is the slant height of the cone.
Given:
- The diameter of the cone is 8 feet, so the radius \(r\) is half of that:
\[ r = \frac{8}{2} = 4 \text{ feet} \]
- The slant height \(l\) is 5 feet.
Now we can calculate the lateral surface area of one cone:
\[ A = \pi r l = 3.14 \times 4 \times 5 \]
Calculating that step-by-step:
\[ A = 3.14 \times 4 = 12.56 \]
\[ A = 12.56 \times 5 = 62.8 \text{ square feet} \]
This is the surface area for one cone. Since there are two cones, we multiply by 2:
\[ \text{Total surface area} = 2 \times 62.8 = 125.6 \text{ square feet} \]
It seems I’ve calculated the total surface area incorrectly. I need to check my options, as the question asks for the area of the outside of the sculpture, which is the lateral area of both cones without the base areas because they meet at the top point.
Looking again at the provided options—226.08 square feet, 653.12 square feet, 113.04 square feet, 326.56 square feet—I see that the results we have calculated (125.6) is not in the options.
Let’s cross-check:
- We calculated \(A = \pi r l = 3.14 \cdot 4 \cdot 5 = 62.8 , \text{square feet (one cone)}\)
- So \(2 \text{ cones} = 125.6 , \text{square feet}\) total.
It appears that we have evaluated correctly, however no option provided fits to derived value. The assumptions about surface area (including totals) need matching to options as they can sometimes be rounded in real-world scenarios. Therefore cross checks, revisits were necessary, but the total distinctly does not match.
Nevertheless, checking misunderstanding might regard if parts of surfaces were to be inclusive, on additions or materials factored under rounding errors present ideally inherent onwards.
Final review should head towards:
\[ \text{Total surface area = } 125.6 \text{ sq. ft. fits no option.} \]
Thus, kindly cross-check question submissions or hover on dimensional descriptions distinctively if segments or half surfaces were alluded incorrectly in language.
For rendering consciously calculated values propose to check outwardly, as selections therein thus would yield confusion in what rightly are presented segments at totals for conclusion posits.