A designer is creating a modern art sculpture of an hourglass 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 steel is needed for the outside of the sculpture, if the slant height of each cone is 5 feet and the diameter is 8 feet. Use 3.14 for pi.(1 point)

Question

Responses

113.04 square feet
113.04 square feet

653.12 square feet
653.12 square feet

226.08 square feet
226.08 square feet

326.56 square feet

Answer 1

To find the surface area of the outside of the sculpture, we need to find the surface area of each cone and then add them together.

The formula for the surface area of a cone is:
Surface Area = π(radius)(slant height)

First, let's find the radius. The diameter is given as 8 feet, so the radius is half of that: 8/2 = 4 feet.

Now, let's find the surface area of one cone:
Surface Area = 3.14(4)(5)
Surface Area = 62.8 square feet

Since there are two cones in the hourglass, we need to double this surface area:
Surface Area of both cones = 62.8 + 62.8 = 125.6 square feet

So, the modern art sculpture of an hourglass would require 125.6 square feet of steel for the outside.