What is the surface area of a right rectangular prism where each edge length measures 13.5 cm
The surface area of a rectangular prism can be found by adding the areas of all its faces.
A right rectangular prism has 6 faces: 2 congruent rectangles for the top and bottom, and 4 congruent rectangles for the sides.
Given that each edge length of the prism measures 13.5 cm, the dimensions of each face will be:
- The top and bottom rectangles will have dimensions 13.5 cm (length) and 13.5 cm (width).
- The side rectangles will have dimensions 13.5 cm (height) and 13.5 cm (width).
The area of each rectangle is found by multiplying its length by its width.
For the top and bottom rectangles:
Area = 13.5 cm * 13.5 cm = 182.25 cm²
For the side rectangles:
Area = 13.5 cm * 13.5 cm = 182.25 cm²
Since there are 2 top/bottom rectangles and 4 side rectangles, the total surface area is given by:
Total surface area = 2 * (Area of top/bottom rectangle) + 4 * (Area of side rectangle)
Total surface area = 2 * 182.25 cm² + 4 * 182.25 cm²
Total surface area = 2 * 182.25 cm² + 729 cm²
Total surface area = 364.5 cm² + 729 cm²
Total surface area = 1093.5 cm²
Therefore, the surface area of the right rectangular prism is 1093.5 cm².
Given that each square is 1 inch, find the surface area of this 4x4 rubix cube
A standard Rubik's Cube consists of 6 faces, each made up of 9 smaller squares. In this case, the cube is a 4x4 Rubik's Cube.
To find the surface area, we need to find the area of each face and then sum them up.
Since each side is 4 squares by 4 squares, the area of each face is 4 * 4 = 16 square inches.
Since there are 6 faces, the total surface area will be 6 * 16 = 96 square inches.
Therefore, the surface area of a 4x4 Rubik's Cube is 96 square inches.