To find the surface area of the hourglass sculpture made of two cones, we first need to calculate the 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 and \( l \) is the slant height.
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Calculating the radius:
The diameter of the cone is 8 feet, so the radius \( r \) is half of that: \[ r = \frac{8}{2} = 4 \text{ feet} \] -
Finding the slant height:
The slant height \( l \) is given as 5 feet. -
Calculating the surface area of one cone:
Using \( \pi \approx 3.14 \), \[ A = \pi r l = 3.14 \times 4 \times 5 \] \[ A = 3.14 \times 20 = 62.8 \text{ square feet} \] -
Calculating the total surface area for two cones:
\[ \text{Total Surface Area} = 2 \times 62.8 = 125.6 \text{ square feet} \]
The correct answer is not listed among the options presented. However, if the question were to ask for the total area of the outside of the sculpture, we would consider both the lateral area (without the base) of the two cones, which gives us:
- The total surface area of the two cones is \( 125.6 \) square feet.
Note that if you included the bases and aimed for a full surface area calculation, you would need to adjust this calculation. But based on lateral area alone, \( 125.6 \text{ square feet} \) is correct.
However, if just lateral area is considered, the expected total for outer surfaces won't match your provided options (e.g., 113.04, 226.08, 326.56, 653.12). Perhaps check that the bases of the cones should not be included or that a typographical error exists in the options.
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