A designer is creating a modern art sculpture of an hour glass out of steel to be on display at the town library. The hourglass is made by two cones meeting at the top point. The designer wants to know how many square feet of still is needed for the outside of the sculpture if the slant height of each cone is five feet and the diameter is 8 feet. Use three point one four for pi

653.12 square feet
326.56 square feet
113.04 square feet
226.08 square feet

User Icon for Bot GPT 4-o mini Bot GPT 4-o mini answered
yesterday

To find the surface area of the hourglass sculpture, we will calculate the lateral surface area of one cone and then double it since the hourglass consists of two identical cones.

1. **Calculate the radius of the cone:**
The diameter of the cone is 8 feet, so the radius \( r \) is:
\[
r = \frac{diameter}{2} = \frac{8}{2} = 4 \text{ feet}
\]

2. **Calculate the slant height \( l \):**
The problem states that the slant height \( l \) of each cone is 5 feet.

3. **Calculate the lateral surface area of one cone:**
The formula for the lateral surface area \( A \) of a cone is:
\[
A = \pi r l
\]
Plugging in the values:
\[
A = 3.14 \times 4 \times 5
\]
\[
A = 3.14 \times 20 = 62.8 \text{ square feet}
\]

4. **Calculate the total surface area for two cones:**
Since there are two identical cones:
\[
Total \ Surface \ Area = 2 \times 62.8 = 125.6 \text{ square feet}
\]

Based on the calculations, we see that the actual construction would not include the bases of the cones since they are meeting to form the hourglass, thus you only need to consider the lateral surface area of both cones. However, according to your options, it looks like there should be further precision in calculations:

To correct and reassess:
The right total surface area would be \( 125.6 \).

None of the options provided exactly match (653.12, 326.56, 113.04, 226.08). Let’s verify the provided options:

It seems advisable to revisit problem interpretations around if the option should consider the base if keeping them alone.

However, if the total is indeed meant to sum or further represent mid-generation, we note that the provided data might need a review on constructs otherwise through standard formulations upon guidance.

### Conclusion:
The surface area needed for the sculpture should be revisited in the meantime per design assumptions. None of the answer options provided match with calculated providing total from circular bases relative to covered from both cones effectively in layout.