A piece of chocolate candy, composed of two congruent triangular prisms like the one shown below, is filled with caramel.
Note: Figure is not drawn to scale.
If a = 1.6 cm, b = 1.1 cm, and c = 2.3 cm, how much caramel can fit inside the piece of candy?
To find the volume of the piece of candy, we first need to find the volume of one of the triangular prisms and then multiply it by 2 since there are two prisms in the candy.
The volume of a triangular prism can be calculated using the formula: V = 0.5 * b * a * h, where b and a are the base and height of the triangle, and h is the height of the prism.
Given that a = 1.6 cm and b = 1.1 cm, we can find the area of the triangle:
Area = 0.5 * 1.1 cm * 1.6 cm = 0.88 cm^2
Now, we need to find the volume of the triangular prism, using c = 2.3 cm as the height:
V = 0.5 * 1.1 cm * 1.6 cm * 2.3 cm = 2.024 cm^3
Since there are two congruent triangular prisms in the candy, the total volume of the candy is:
Total Volume = 2 * 2.024 cm^3 = 4.048 cm^3
Therefore, the piece of candy can fit 4.048 cm^3 of caramel inside.