Question

The figure below shows a large block of cheese.

The cheese block has 2 triangular faces each with base length 6 inches and height 10 inches, 2 rectangular faces each with a length of 4 inches and 10 inches wide, and a rectangular base of length 4 inches and width 6 inches.

What is the volume of the block of cheese?

A.
120 cubic inches

B.
64 cubic inches

C.
46 cubic inches

D.
240 cubic inches

Answer 1

To calculate the volume of the block of cheese, we need to determine the dimensions of the solid. The block seems to be a prism with a triangular face.

1. **Calculate the area of one triangular face:**
The area \( A \) of a triangle can be calculated using the formula:
\[
A = \frac{1}{2} \times \text{base} \times \text{height}
\]
Here, the base is 6 inches and the height is 10 inches:
\[
A = \frac{1}{2} \times 6 \, \text{inches} \times 10 \, \text{inches} = \frac{1}{2} \times 60 = 30 \, \text{square inches}
\]

2. **Identify the height of the prism:**
The height of the prism can be represented by the length of the rectangular side, which is given as 4 inches.

3. **Calculate the volume of the prism:**
The volume \( V \) of a prism is given by:
\[
V = \text{Base Area} \times \text{Height}
\]
where the Base Area is the area of the triangular face and Height is the height of the prism.

So, plugging in the values we computed:
\[
V = 30 \, \text{square inches} \times 4 \, \text{inches} = 120 \, \text{cubic inches}
\]

Thus, the volume of the block of cheese is:
\[
\boxed{120} \, \text{cubic inches}
\]