The missing dimension of the rectangular prism is 12 inches, and the calculated volume is 432 cubic inches using the dimensions provided (6 inches, 6 inches, and 12 inches).
To find the missing dimension and subsequently calculate the volume of the rectangular prism, we can use the information provided. The known dimensions are given as 6 inches, 6 inches, and x inches.
The area of the shaded face, l times w, is given as 72 square inches. We can set up an equation using the known dimensions:
6 times 6 equals 36 square inches.
The area is also expressed as l times w, where l and w are the two known dimensions. Setting this equal to the given area of 72 square inches, we have:
6 times x equals 72.
Solving for x, we find that x is equal to 12 inches. Now that we have all three dimensions (6 inches, 6 inches, and 12 inches), we can calculate the volume of the rectangular prism using the formula V equals l times w times h:
V equals 6 times 6 times 12, which is equal to 432 cubic inches.
Therefore, the missing dimension is found to be 12 inches, and the volume of the rectangular prism is 432 cubic inches.
The question probable may be:
The area of the shaded face is 72 square inches. The length of the missing dimension is in. The volume of the rectangular prism is in^3 Try again.