carlos makes geometrical artworks out of sheet metal. the dimensions of a full size sculpture will be 6 times the dimensions of the model shown below. He will not use any metal for the bottom base of the cylinder. How many square feet of sheet metal will carlos use for the fully size sculpture.

the circular shape on the top is 3 in high and 10 in wide and sits directly on top of a square that measures 10 in high and 10 in wide.

Your description is not clear. At first I read it as a cylinder sitting on top of a cube.

Then you talk about a circular shape on the top.
I can't visualize it
Are there two questions here ?

I wish I can upload a photo. visualize it like a round metal cake pan on top of a metal box That the only way I can describe it.

To calculate the amount of sheet metal Carlos will use, we need to find the surface area of each individual shape and then multiply it by 6 (since the full-size sculpture will be 6 times the size of the model).

Let's start with the square base. The surface area of a square is given by the formula:
Surface Area = side length^2

For the model, the side length of the square base is 10 inches. Therefore, the surface area of the model's square base is:
Surface Area of model's square base = 10^2 = 100 square inches

Since Carlos will not use any metal for the bottom base of the cylinder, we do not need to calculate its surface area.

Now, let's move on to the circular shape on the top. The surface area of a cylinder's curved surface is given by the formula:
Surface Area = 2π(radius)(height)

For the model, the radius is half the width of the circular shape, which is 10 inches. The height of the cylinder is given as 3 inches. Therefore, the surface area of the model's circular shape is:
Surface Area of model's circular shape = 2π(10)(3) = 60π square inches

To find the total surface area of the model, we sum up the surface areas of the square base and the circular shape:
Total surface area of model = Surface Area of model's square base + Surface Area of model's circular shape
= 100 + 60π square inches

Since the full-size sculpture will be 6 times the size of the model, we multiply the surface area of the model by 6 to find the surface area of the full-size sculpture:
Total surface area of full-size sculpture = 6 * (Total surface area of model)
= 6 * (100 + 60π) square inches

So, Carlos will use 6 * (100 + 60π) square inches of sheet metal for the fully size sculpture.

To find the amount of sheet metal that Carlos will use for the full-size sculpture, we need to calculate the surface area of each component and then multiply it by 6.

Let's start by calculating the surface area of the circular shape at the top:

The circular shape is a cylinder with a height of 3 inches and a diameter of 10 inches (which means the radius is 10/2 = 5 inches). Since Carlos won't be using any metal for the bottom base of the cylinder, we only need to calculate the surface area of the curved part.

The formula for the surface area of a cylinder is: A = 2πrh, where A is the surface area, π is a mathematical constant (approximately 3.14), r is the radius, and h is the height.

In this case, the surface area of the curved part is: A = 2π(5 inches)(3 inches) = 30π square inches.

Next, let's calculate the surface area of the square base:

The square base measures 10 inches in height and 10 inches in width. The surface area of a square is simply the width multiplied by the height, so in this case, the surface area is: A = 10 inches * 10 inches = 100 square inches.

Now, let's calculate the total surface area of both components:

Total surface area = Surface area of circular shape + Surface area of square base
= 30π square inches + 100 square inches.

Finally, since the dimensions of the full-size sculpture are 6 times the dimensions of the model, we need to multiply the total surface area by 6:

Total surface area of the full-size sculpture = 6 * (30π + 100) square inches.

To convert this into square feet, we need to divide by 144 (since there are 144 square inches in a square foot):

Total surface area of the full-size sculpture in square feet = (6 * (30π + 100)) / 144 square feet.

So, to find how many square feet of sheet metal Carlos will use for the fully sized sculpture, we need to evaluate the above expression.