A rectangular prism is 18 inches tall and has a square base whose length is 9 inches. Oliver plans to cover the top and bottom of the rectangular prism with material A, which costs 2 cents per square inch. He then plans to cover the other four faces of the prism with material B, which costs 1.5 cents per square inch. How much money will Oliver spend on the materials to cover the rectangular prism?
base area = 9^2 = 81
each face has area 9*18 = 162
now just multiply each area by its cost and add up the proper number of faces.
To find out how much money Oliver will spend on the materials to cover the rectangular prism, we need to calculate the total surface area of the prism and then multiply it by the respective costs per square inch.
The rectangular prism has a height of 18 inches, and its base is a square with a length of 9 inches. Therefore, the dimensions of the base are 9 inches by 9 inches.
The total surface area of a rectangular prism can be found by adding the areas of all its faces. In this case, we have two identical bases, each with an area of 9 inches by 9 inches, and four identical lateral faces, each with an area of 9 inches by 18 inches.
The total surface area of the bases is 2 * (9 inches * 9 inches) = 162 square inches.
The total surface area of the lateral faces is 4 * (9 inches * 18 inches) = 648 square inches.
To find the total surface area of the rectangular prism, we add the areas of the bases and the lateral faces: 162 square inches + 648 square inches = 810 square inches.
Now, we can calculate the cost of material A, which covers the top and bottom of the prism. The cost for material A is 2 cents per square inch. So, the cost of material A is 2 cents * 810 square inches = 1620 cents.
Next, we can calculate the cost of material B, which covers the four lateral faces of the prism. The cost for material B is 1.5 cents per square inch. So, the cost of material B is 1.5 cents * 648 square inches = 972 cents.
Finally, we add the costs of material A and material B to find the total amount Oliver will spend on the materials to cover the rectangular prism: 1620 cents + 972 cents = 2592 cents.
Therefore, Oliver will spend 2592 cents, or $25.92, on the materials to cover the rectangular prism.