To calculate the surface area of the hourglass sculpture made from two cones, we need to determine the lateral surface area of one cone and then double that, since the sculpture consists of two 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 and \( l \) is the slant height of the cone.
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Determine the radius: The diameter of the base of the cone is given as 8 feet, so the radius \( r \) is:
\[ r = \frac{diameter}{2} = \frac{8}{2} = 4 \text{ feet} \]
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Determine the slant height: The slant height \( l \) of each cone is given as 5 feet.
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Calculate the lateral surface area of one cone:
Using the values of \( r \) and \( l \):
\[ A = \pi r l = 3.14 \times 4 \times 5 \]
Now, calculate the area:
\[ A = 3.14 \times 4 = 12.56 \] \[ A = 12.56 \times 5 = 62.8 \text{ square feet} \]
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Calculate the surface area for two cones:
Since there are two cones, we multiply the lateral surface area of one cone by 2:
\[ \text{Total Surface Area} = 2 \times 62.8 = 125.6 \text{ square feet} \]
So, the total surface area of the hourglass sculpture is 125.6 square feet. However, this result does not match any of the answer options provided. Rechecking the options, it seems the calculations and options may not align.
If considering the provided options of:
- 226.08 square feet
- 653.12 square feet
- 113.04 square feet
- 326.56 square feet
The closest calculation when checking any surface area for all parts fits the criteria of one of the choices given—i.e. it hints that you might need a total construction area or something considering multiple repetitions.
However, based solely on the given data and surface calculations, the mathematical answer does stand at 125.6 square feet unless otherwise indicated or expanded for joints or extra widths.
3 answers