A rectangular block with a volume of 250 cm3 was sliced into two cubes of equal volume. How much greater (in sq.cm) is the combined surface area of the two cubes than the original surface area of the rectangular block?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 50 cm2
The block is cut into two equal cubes, so each cube has half its volume, and the block is the two cubes placed side by side.
The sizes:
Volume of each cube \(=\frac{250}{2}=125\) cm3, so its side is \(\sqrt[3]{125}=5\) cm
The block is \(10\times5\times5\) cm
The surface areas:
Block: \(2(10\times5+5\times5+10\times5)=2(125)=250\) cm2
Two cubes: \(2\times6\times5^{2}=300\) cm2
Increase: \(300-250=\) 50 cm2
Shortcut:
Cutting the block leaves every old face where it was and adds two new faces, one on each cube, where the cut is made
Each new face is a square of side 5 cm, so the increase is \(2\times25=50\) cm2