Question

in the picture, the mass of the block is 200 g, the dimensions of the block are 6 cm by 4 cm by 5 cm. what is its density? options: 13.33 g/cm³, 24000 g/cm³, 0.60 g/cm³, 1.67 g/cm³ (image shows a rectangular block with mass = 200g, length 6 cm, width 4 cm, height 5 cm)

Explanation:

Step1: Calculate the volume of the block

The block is a rectangular prism, and the volume \( V \) of a rectangular prism is given by the formula \( V = l \times w \times h \), where \( l = 6 \, \text{cm} \), \( w = 4 \, \text{cm} \), and \( h = 5 \, \text{cm} \).
\[
V = 6 \times 4 \times 5 = 120 \, \text{cm}^3
\]

Step2: Calculate the density

Density \(
ho \) is defined as mass \( m \) divided by volume \( V \), i.e., \(
ho=\frac{m}{V} \). Given \( m = 200 \, \text{g} \) and \( V = 120 \, \text{cm}^3 \).
\[

ho=\frac{200}{120}\approx1.67 \, \text{g/cm}^3
\]
Wait, there is a mistake above. Wait, let's recalculate. Wait, \( 200\div120 = \frac{5}{3}\approx1.67 \)? Wait, no, wait the options: Wait, maybe I miscalculated the volume? Wait, 645: 64=24, 245=120. Then mass is 200g. So density is 200/120 = 5/3 ≈1.67? But wait, let's check the options again. Wait, the orange option is 0.60, green 13.33, purple 24000, cyan 1.67. Wait, maybe I made a mistake. Wait, no, density formula is mass over volume. So 200g divided by 120 cm³. Let's compute 200 ÷ 120: 200 ÷ 120 = 1.666... ≈1.67 g/cm³. So the correct option should be the cyan one with 1.67 g/cm³. Wait, but let's check again. Wait, maybe the dimensions are different? Wait, the block is 6 cm by 4 cm by 5 cm. So volume is 645=120 cm³. Mass is 200g. So density is 200/120 ≈1.67 g/cm³. So the answer is the option with 1.67 g/cm³.

Wait, but in my first calculation, I thought maybe I messed up, but no. So the correct answer is 1.67 g/cm³.

Answer:

The option with \( 1.67 \, \text{g/cm}^3 \) (the cyan - colored option, assuming the last option is \( 1.67 \, \text{g/cm}^3 \))