To find the surface area of the hourglass sculpture made by two cones, we need to calculate the lateral surface area of one cone and then double that since there are 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 of the cone, and \( l \) is the slant height of the cone.
Given:
- The diameter of the cone is 8 feet, so the radius \( r \) is:
\[ r = \frac{diameter}{2} = \frac{8}{2} = 4 \text{ feet} \]
- The slant height \( l \) is 5 feet.
Now plug these values into the formula for the lateral surface area of one cone:
\[ A = \pi r l = 3.14 \times 4 \times 5 \]
Calculating this:
\[ A = 3.14 \times 4 = 12.56 \] \[ A = 12.56 \times 5 = 62.8 \text{ square feet} \]
This is the lateral surface area for one cone. Since there are two cones, we multiply this result by 2:
\[ \text{Total surface area} = 2 \times 62.8 = 125.6 \text{ square feet} \]
Based on the calculations, none of the provided response options match the calculated total surface area. If there is any ambiguity or you would like to double-check the parameters or calculations, please let me know!
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