To determine the weight of the water displaced by a block of iron with given dimensions, follow these steps:
1. Calculate the Volume of the Iron Block:
The volume ([tex]\( V \)[/tex]) of a rectangular block is found by multiplying its length ([tex]\( l \)[/tex]), width ([tex]\( w \)[/tex]), and height ([tex]\( h \)[/tex]) together.
[tex]\[
V = l \times w \times h
\][/tex]
Given:
[tex]\[
l = 3.00 \, \text{cm}, \quad w = 3.00 \, \text{cm}, \quad h = 3.00 \, \text{cm}
\][/tex]
[tex]\[
V = 3.00 \times 3.00 \times 3.00 = 27.00 \, \text{cm}^3
\][/tex]
2. Determine the Mass of the Displaced Water:
Since the iron block will displace an equal volume of water, we need to calculate the mass of this water. The mass ([tex]\( m \)[/tex]) is found by multiplying the volume by the density ([tex]\( \rho \)[/tex]) of water.
Given the density of water:
[tex]\[
\rho = 1.00 \, \text{g/cm}^3
\][/tex]
[tex]\[
m = V \times \rho = 27.00 \, \text{cm}^3 \times 1.00 \, \text{g/cm}^3 = 27.00 \, \text{g}
\][/tex]
3. Convert the Mass to Kilograms:
The mass must be converted to kilograms to use the formula for weight. There are 1000 grams in a kilogram.
[tex]\[
m_{\text{kg}} = \frac{m}{1000} = \frac{27.00 \, \text{g}}{1000} = 0.027 \, \text{kg}
\][/tex]
4. Calculate the Weight of the Displaced Water:
The weight ([tex]\( W \)[/tex]) of the water displaced can be calculated using the formula [tex]\( W = m \times g \)[/tex], where [tex]\( g \)[/tex] is the acceleration due to gravity.
Given [tex]\( g = 9.80 \, \text{m/s}^2 \)[/tex]:
[tex]\[
W = m_{\text{kg}} \times g = 0.027 \, \text{kg} \times 9.80 \, \text{m/s}^2 = 0.2646 \, \text{N}
\][/tex]
Hence, the weight of the water displaced by the block of iron is [tex]\( 0.2646 \, \text{N} \)[/tex], which approximates to [tex]\( 0.265 \, \text{N} \)[/tex].
