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

1 answer

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: \[ \boxed{120} , \text{cubic inches} \]