Subject: General Aptitude · Chapter: Volume and Surface Area · Exam: · Marks: · Difficulty:
A rectangular block with a volume of $250 \mathrm{cm}^{3}$ was sliced into two cubes of equal volume. How much greater (in sq. cm) is the combined surface area of the two cubes then the original surface area of the rectangular block?
(a)48.64
(b)50
(c)56.25
(d)84.67
Answer
Answer (as printed): B
Explanation
Clearly, when the rectangular block was cut into 2 identical cubes, two new faces were formed - one on each cube along the line of the cut. So, the difference in surface areas is equal to the surface area of the newly formed faces. $$\text { Volume of each cube }=\left(\frac{250}{2}\right) \mathrm{cm}^{3}=125 \mathrm{cm}^{3} .$$ Edge of each cube $=\sqrt[3]{125} \mathrm{cm}=5 \mathrm{cm}$. Hence, difference in surface areas $=\left(2 \times 5^{2}\right) \mathrm{cm}^{2}=50 \mathrm{cm}^{2}$.