25. A metal cube with an edge of one foot is melted into rectangular solid one-eighth of a foot in height. What is the area of the top of the top of the new solid.


Please show work/explain

A. 1/64 sq.ft.
B. 1/8 sq.ft.
C. 1/4 sq.ft.
D. 4 sq.ft.
E. 8 sq.ft.

The cube is 1ft x 1ft x 1ft, so what is the volume?

The rectangular solid is (1/8) ft x width x length. I'm not sure any assumptions can be made about the width and length. Does the question include any additional details?

since the volume is 1, and the height is now 1/8, the surface area of the two bases is 8

v = Bh = 8(1/8)

To find the area of the top of the new solid, we need to determine the dimensions of the rectangular solid.

Given that the original metal cube has an edge of one foot, its volume is (1 ft)³ = 1 ft³.

Since this cube is melted and formed into a rectangular solid with a height of one-eighth of a foot, we can determine the volume of the new solid as well.

The volume of a rectangular solid is given by V = l × w × h, where l, w, and h represent the length, width, and height respectively.

In this case, the height (h) of the new solid is one-eighth of a foot, so h = 1/8 ft.

We know that the volume of the metal cube is equal to the volume of the new solid, so:

1 ft³ = l × w × (1/8) ft

Multiplying both sides of the equation by 8, we get:

8 ft³ = 8l × w

Now, we'll find the area of the top of the rectangular solid by multiplying the length (l) and width (w) of the new solid.

Dividing both sides of the equation by 8, we have:

l × w = 1 ft²

Therefore, the area of the top of the new solid is 1 square foot (1 ft²).

Thus, the correct answer is C. 1/4 sq.ft.