Problem Solving

Q. . A rectangular block with a volume of 250 cubic inches was sliced into 2 cubes of equal volume. How much greater, in square inches, is the combined surface area of the 2 cubes that the original surface area of the rectangular block?
A. 5;
B.10;
C.25;
D.50;
E.100

The question says that the rectangular block was sliced into two cubes. So before being sliced, the rectangular block had to be in the shape of two cubes put together.

The volume of the rectangular block = combined volume of the two cubes = 250 cubic inches. So the volume of each cube is 250/2 = 125 cubic inches.

The lengths of the edges of the cubes are therefore ∛125 = 5.

So the rectangular block is made of two cubes with edges length 5.

That means that the block is 5 x 5 x 10.

The faces of the rectangular block are made up of faces of the cubes.

The difference between the surface area of the block and that of the two cubes is the combined area of the two faces pf the cubes where the slice happened. Those two faces are not faces of the block.

The area of a face of one of the cubes is 5 x 5 = 25.

The area of two faces is 25 x 2 = 50.

The correct answer is D.

Joy Shaha wrote:Q. . A rectangular block with a volume of 250 cubic inches was sliced into 2 cubes of equal volume. How much greater, in square inches, is the combined surface area of the 2 cubes that the original surface area of the rectangular block?
A. 5;
B.10;
C.25;
D.50;
E.100

Since the rectangular block is sliced in two cubes, hence volume of the cube = 125 inch cube
Volume of the cube = a^3 = 125
Hence side of the cube = 5

Area of one face = 5*5 = 25
Total surface area = 6*25 = 150 inch square
Surface area of two cubes = 150*2 = 300 inch square

Sides of the rectangular block = 10, 5, 5
Hence surface area = 10*5 + 10*5 + 10*5 + 10*5 + 5*5 + 5*5 = 200 + 25 + 25 = 250

Difference in area = 50

Correct Option: D

Each cube has volume 125, so each edge length is 5, and the surface area of each cube = 6 * 5 * 5 = 150. We've got two of them, so our total = 300.

That means that the original rectangle had sides of 10, 5, and 5, so its surface area was 10*5 + 10*5 + 10*5 + 10*5 + 5*5 + 5*5 = 250.

300 - 250 = 50, so we're set.