A cube of length 1 cm is taken out from a cube of length 8 cm. What is the weight of the remaining portion?

### Concept & Volume Proportionality For uniform solid objects, weight is directly proportional to volume. The fraction of the remaining weight will be equal to the fraction of the remaining volume. $$ \text{Volume of a Cube} = \text{side}^3 $$ ### Step-by-Step Solution * Find the volume of the original cube: Side = $8\text{ cm}$. Volume = $8^3 = 512\text{ cm}^3$. * Find the volume of the removed cube: Side = $1\text{ cm}$. Volume = $1^3 = 1\text{ cm}^3$. * Calculate the remaining volume: $512 - 1 = 511\text{ cm}^3$. * Determine the weight ratio: Since weight correlates with volume, the remaining weight is $\frac{511}{512}$ of the original weight. ### Exam Strategy & Shortcut Just look at the cubes of the dimensions: $1^3$ vs $8^3$. The volumes are 1 and 512. The remainder is $512 - 1 = 511$. The ratio is automatically $\frac{511}{512}$. ### Common Pitfall Mistaking the relationship between linear dimensions and volume/weight. Some might just subtract the lengths ($8 - 1 = 7$) and incorrectly choose $\frac{7}{8}$. ### Final Answer Therefore, the correct answer is **$\frac{511}{512}$ of the weight of the original cube**.