To calculate the surface area of the cube and square pyramid, we need to find the area of each face and add them together:
1. Surface area of the cube:
- The cube has 6 faces, all of which are squares.
- If the length of each side of the cube is "s," then the area of each face is s^2.
- So, the total surface area of the cube is 6s^2.
2. Surface area of the square pyramid:
- The square pyramid has 5 faces - 1 square base and 4 triangular faces.
- If the base of the square pyramid has side length "s," then the area of the base is s^2.
- The area of each triangular face can be calculated using the formula for the area of a triangle: 0.5 * base * height.
- The height of the pyramid can be calculated using the Pythagorean theorem as h = sqrt(s^2 + (0.5s)^2) = sqrt(5/4) * s.
- So, the area of each triangular face is 0.5 * s * sqrt(5/4) * s = 0.5 * sqrt(5) * s^2.
- Therefore, the total surface area of the square pyramid is s^2 + 4 * (0.5 * sqrt(5) * s^2).
Adding the surface areas of the cube and square pyramid together:
Total surface area = 6s^2 + s^2 + 4 * (0.5 * sqrt(5) * s^2)
= 7s^2 + 2 * sqrt(5) * s^2
= (7 + 2 * sqrt(5)) * s^2
Now, if each side of the cube has a length of 10 cm (for example):
Total surface area = (7 + 2 * sqrt(5)) * 10^2
≈ (7 + 2 * 2.236) * 100
≈ 11.472 * 100
≈ 1147.2 cm^2
Given the surface area of the toy, we would need to calculate the amount of paint required for each cm^2 and then multiply it by the total surface area.
Graham carves a block of wood shaped like a cube with a square pyramid on top. How much paint will Graham need to paint the toy?
1 answer
1 answer