Question

A designer is creating a modern art sculpture of an hourglass out of steel to be on display at the town brary The hourglass is made by we cones meeting at the top point. The designer wants to know how many square feet of steel is needed for the outside of the sculpture at eg of each cone is 5 feet and the diameter is 8 feet Use 3 14 for pi (1 point)

553 12 square feet

Answer 1

To calculate the total surface area of each cone, we need to calculate the lateral surface area of each cone and then add them together.

The lateral surface area of a cone can be found using the formula A = πrℓ, where A is the lateral surface area, r is the radius, and ℓ is the slant height.

Given that the diameter of each cone is 8 feet, the radius would be half of that, which is 4 feet. And the length of the slant height can be found using the Pythagorean theorem.

We can find the slant height ℓ using the formula:

ℓ = √(r^2 + h^2)

Where r is the radius and h is the height of each cone.

Given that the height of each cone is 5 feet, we can calculate ℓ:

ℓ = √(4^2 + 5^2)
ℓ = √(16 + 25)
ℓ = √(41)
ℓ ≈ 6.40

Now we can calculate the surface area of each cone:

A = πrℓ
A = 3.14 × 4 × 6.40
A ≈ 80.256

Since there are two cones in the hourglass, we need to calculate the total surface area:

Total surface area = 2 × A
Total surface area = 2 × 80.256
Total surface area ≈ 160.512 square feet

Therefore, the designer would need approximately 160.512 square feet of steel for the outside of the sculpture.