Question

(01.03 mc)
three blocks are shown:
block a
diagram: 8 cm length, 2 cm, 1 cm, mass 3 kg
block b
diagram: 1 cm, 2 cm, 8 cm height, mass 4 kg
block c
diagram: 8 cm, 2 cm, 1 cm, mass 4 kg
which statement is correct?
○ the density of block b is equal to the density of block c.
○ block a has the greatest density.
○ block b has the least density.
○ the density of block a is equal to the density of block b.

Explanation:

Step1: Recall density formula

Density formula is $
ho = \frac{m}{V}$, where $m$ is mass and $V$ is volume. For a rectangular block, volume $V = l \times w \times h$.

Step2: Calculate volume of Block A

Block A: $l = 8\ cm$, $w = 2\ cm$, $h = 1\ cm$. So $V_A = 8 \times 2 \times 1 = 16\ cm^3$. Mass $m_A = 3\ kg$. Density $
ho_A = \frac{3}{16} = 0.1875\ kg/cm^3$.

Step3: Calculate volume of Block B

Block B: $l = 1\ cm$, $w = 2\ cm$, $h = 8\ cm$. So $V_B = 1 \times 2 \times 8 = 16\ cm^3$. Mass $m_B = 4\ kg$. Density $
ho_B = \frac{4}{16} = 0.25\ kg/cm^3$.

Step4: Calculate volume of Block C

Block C: $l = 8\ cm$, $w = 2\ cm$, $h = 1\ cm$. So $V_C = 8 \times 2 \times 1 = 16\ cm^3$. Mass $m_C = 4\ kg$. Density $
ho_C = \frac{4}{16} = 0.25\ kg/cm^3$.

Step5: Compare densities

• $

ho_B = 0.25$, $
ho_C = 0.25$ → equal.

• $

ho_A = 0.1875$ (less than $
ho_B$ and $
ho_C$), so Block A does not have greatest density.

• $

ho_B = 0.25$ (same as $
ho_C$, greater than $
ho_A$), so Block B does not have least density.

• $

ho_A = 0.1875$, $
ho_B = 0.25$ → not equal.

Answer:

The density of Block B is equal to the density of Block C.