A piece of cheese is a prism. The cross-section is a sector of a circle of radius 12 cm and angle 32 degree. The height of the piece of cheese is 5 cm. Calculate the total surface area?
To calculate the total surface area of the piece of cheese, we need to find the lateral surface area of the prism and the two circular bases.
First, let's find the lateral surface area. The lateral surface area of a prism can be calculated by the formula:
Lateral Surface Area = perimeter of the base * height
The perimeter of the base in this case is the circumference of the circle sector, which can be calculated as:
2 * π * radius * (angle in radians / 2π)
= 2 * π * 12 * (32°/360°)
= 2 * π * 12 * (8π/90)
= 2 * 12 * 8/9
= 16.88 cm
Now, we can calculate the lateral surface area:
Lateral Surface Area = 16.88 * 5
= 84.4 cm²
Next, let's find the total surface area by adding the area of the two circular bases. The area of each circular base can be calculated as:
Area of a circle = π * radius^2
= π * 12^2
= π * 144
= 452.39 cm²
Therefore, the total surface area of the piece of cheese is:
Total Surface Area = 2 * 452.39 + 84.4
= 904.78 + 84.4
= 989.18 cm²
So, the total surface area of the piece of cheese is 989.18 cm².