A square block of steel with volume 10 cm3 and mass of 75 g is cut precisely in half. The density of the two smaller pieces is now...

Question

A.
the same as the original density.
B.
one-fourth the original density.
C.
one-half the original density.
D.
two times the original density.

Answer 1

To find the density of the two smaller pieces after the steel block is cut in half, we first need to calculate the original density of the block.

Density is defined as mass divided by volume:

\[ \text{Density} = \frac{\text{Mass}}{\text{Volume}} \]

Given that the mass of the original block is 75 g and the volume is 10 cm³, we can calculate the original density:

\[ \text{Original Density} = \frac{75 , \text{g}}{10 , \text{cm}^3} = 7.5 , \text{g/cm}^3 \]

When the block is cut in half, each of the two smaller pieces will have:

• Mass: \( \frac{75, \text{g}}{2} = 37.5 , \text{g} \)
• Volume: \( \frac{10, \text{cm}^3}{2} = 5 , \text{cm}^3 \)

Now we can calculate the density of one of the smaller pieces:

\[ \text{Density of smaller piece} = \frac{37.5 , \text{g}}{5 , \text{cm}^3} = 7.5 , \text{g/cm}^3 \]

Since the density of each smaller piece is the same as the original density, the answer is:

A. the same as the original density.