To find the surface area of the hourglass sculpture made of two cones, we first need to calculate the lateral surface area of one cone and then double that for both cones since they are identical.
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.
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Calculate the radius:
- The diameter of the cone is given as 8 feet, so the radius \( r \) is: \[ r = \frac{diameter}{2} = \frac{8 \text{ feet}}{2} = 4 \text{ feet} \]
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Use the slant height:
- The slant height \( l \) is given as 5 feet.
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Calculate the lateral surface area of one cone:
- Using \( \pi \approx 3.14 \): \[ A = \pi r l = 3.14 \times 4 \text{ ft} \times 5 \text{ ft} \] \[ A = 3.14 \times 20 \text{ ft}^2 = 62.8 \text{ ft}^2 \]
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Calculate the total surface area for two cones: \[ \text{Total surface area} = 2 \times A = 2 \times 62.8 \text{ ft}^2 = 125.6 \text{ ft}^2 \]
Thus, the total amount of steel needed for the outside of the sculpture is 125.6 square feet.
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