# I am bulding a sculpture out of rock and need help figuring out how much rock to buy... Here are the figures...

1 ton of 1.5" rock covers 107 sq. ft.

My sculpture will be comprised of 24 layers of rock 2" thick. Each layer will be aproximatly 3ft. by 3ft. How many tons of rock do I need?

How does one figure this answer? Thank you.

It doesn't really sound like you are making a sculpture. I don't know of any sculptures that are made with "layers of rock." It's okay to say you want help with a geometry problem that has been assigned. If my knowledge of sculptures is lacking, you have my apologies.

Since the 2" thick rock has 24 layers, you are looking for a depth of 48". 48" divided by 1.5" = 32 layers of 1.5" stone that are needed.

Since each layer is 9 square feet, multiply the layers by 32. Then divide that by 107 to get the number of tons that will be needed.

I hope this helps. Thanks for asking.

Another way to do this is density.
The density of rock is 1ton/volume where volume is 107*(1.5/12) ft^3.

This density will not vary in the second problem. Calculate out the density.

amount of rock = density*24*(2/12)*3*3

## To calculate the amount of rock you need for your sculpture, you can use two different approaches - one using the given coverage area information, and the other using the density of rock.

1. Using the coverage area information:
- The dimensions of each layer are given as approximately 3ft. by 3ft., resulting in an area of 9 square feet.
- Since each layer is 2 inches thick, and you have 24 layers, the total thickness is 48 inches (or 4 feet).
- The given coverage for 1 ton of 1.5" rock is 107 sq. ft.
- Divide the total thickness of the sculpture (4 feet) by the thickness covered by 1 ton of rock (1.5 inches or 0.125 feet) to get the number of layers needed. Therefore, 4 feet divided by 0.125 feet gives you 32 layers of 1.5" rock.
- Multiply the number of layers (32) by the area of each layer (9 sq. ft.) to get the total area of the sculpture - 32 layers * 9 sq. ft. = 288 sq. ft.
- Finally, divide the total area of the sculpture (288 sq. ft.) by the coverage area per ton (107 sq. ft.) to find out how many tons you will need. Therefore, 288 sq. ft. divided by 107 sq. ft. is approximately 2.69 tons.

So, using this method, you will need approximately 2.69 tons of rock.

2. Using the density of rock:
- The density of rock is given as 1 ton/volume.
- The volume can be calculated by multiplying the dimensions of each layer - 24 layers * (2 inches / 12 inches) * 3ft * 3ft.
- Simplify the calculation to get the volume of one layer in cubic feet.
- Multiply the volume of one layer (in cubic feet) by the density (1 ton/volume) to get the amount of rock in tons.
- Therefore, amount of rock = density * 24 * (2/12) * 3 * 3.

By using either method, you will be able to determine the number of tons of rock you need for your sculpture.