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 multiply it by 2 (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,
- \( l \) is the slant height of the cone.
Given:
- The diameter of the cone is 8 feet, so the radius \( r \) is half of that: \[ r = \frac{8}{2} = 4 \text{ feet} \]
- The slant height \( l \) is given as 5 feet.
Now we can calculate the lateral surface area of one cone:
\[ A = \pi r l = 3.14 \times 4 \times 5 \]
Calculating this step by step:
-
First calculate \( 4 \times 5 \): \[ 4 \times 5 = 20 \]
-
Now multiply by \( \pi \): \[ A = 3.14 \times 20 = 62.8 \text{ square feet} \]
Since there are two cones, we multiply this result by 2 to find the total surface area of the hourglass:
\[ \text{Total Surface Area} = 2 \times 62.8 = 125.6 \text{ square feet} \]
However, this excluding the areas where two cones meet. For the two cones forming an hourglass shape, we typically do not include the base area of each cone; therefore, the total area required for the surface of the hourglass is:
The lateral surface area we calculated earlier is for both cones:
So the total surface area of both cones would actually be the same we calculated, since we want the outside surface area of both cones.
Thus the total surface area needed is \( 125.6 \) square feet.
After recalculating the problem, it appears none of your options fit this value. If the calculations were strictly for the two lateral sides of the cones, we would need to confirm why the answer does not match.
However, let's validate the options you provided:
It appears the correct interpretation of the question has been miscounted earlier regarding the necessity to focus purely on the lateral area for the outside.
So after reviewing - both cones combined - if recalibrated to estimate understanding needed for multiple constructs and estimates we have:
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1 answer