To find the volume of the wedge of cheese, we need to follow these steps:
1. Calculate the area of the triangular base:
- The formula to calculate the area of a triangle is [tex]\(\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}\)[/tex].
- Here, the base of the triangle is 10 inches and the height is 5 inches.
- Plugging these values into the formula, we get:
[tex]\[
\text{Area} = \frac{1}{2} \times 10 \times 5 = 25 \text{ square inches}
\][/tex]
2. Calculate the volume of the wedge:
- The volume of a prism is given by the formula [tex]\(\text{Volume} = \text{Base Area} \times \text{height of the prism}\)[/tex].
- Here, the height of the triangular prism (wedge of cheese) is 6 inches.
- Using the base area we calculated in step 1, we get:
[tex]\[
\text{Volume} = 25 \text{ square inches} \times 6 \text{ inches} = 150 \text{ cubic inches}
\][/tex]
So, if you ate this whole block of cheese, you would have eaten 150 cubic inches of cheese (ignoring the holes).
