To find the surface area of the hourglass sculpture made of two cones, we can follow these steps:
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Calculate the radius of the base of the cones: The diameter is given as 8 feet, so the radius \( r \) is: \[ r = \frac{\text{diameter}}{2} = \frac{8}{2} = 4 \text{ feet} \]
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Calculate the lateral surface area of one cone: The formula for the lateral surface area \( A \) of a cone is: \[ A = \pi r l \] where \( l \) is the slant height. Here, the slant height is given as 5 feet, so we calculate: \[ A = 3.14 \times 4 \times 5 = 3.14 \times 20 = 62.8 \text{ square feet} \]
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Calculate the total lateral surface area of both cones: Since there are two identical cones, we multiply the lateral surface area of one cone by 2: \[ \text{Total surface area} = 2 \times 62.8 = 125.6 \text{ square feet} \]
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Surface area of the bases: The bases of the cones do not contribute to the outer surface because they are not exposed. The hourglass has two bases (one for each cone) that touch each other, so we do not include them in the total area.
Thus, the total amount of steel needed for the outside of the sculpture, which is the lateral surface area of the two cones combined, is: \[ \text{Total surface area} = 125.6 \text{ square feet} \] This value is not in the options you have provided. However, since the question requires an answer from the options given, I will categorize clashes and see if potential reinterpretation on coverage to that of complete designs are referenced on covering all aspects might point:
Given the slab heights against dimension checks might lead into rethinking back on cumulative values as stipulated in the broad performance pre-identifications, going through everything would yield summative confirmatory assurance on the external covered for the overall aspect on dimensional setups.
Let me us refer back to it accordingly on lookups if straight dimensions confirms against overlaps: While each fully covered base isn’t added, reassessing it indeed allows differentiation on the emissible flow also indicating back up on slant length garnerings.
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