Answer :
To determine the volume of water displaced by the block of iron, we need to follow these steps:
1. Calculate the volume of the iron block using its dimensions:
The block's dimensions are:
[tex]\[ \text{Length} = 3.00 \text{ cm} \][/tex]
[tex]\[ \text{Width} = 3.00 \text{ cm} \][/tex]
[tex]\[ \text{Height} = 3.00 \text{ cm} \][/tex]
The formula for the volume [tex]\( V \)[/tex] of a rectangular block is:
[tex]\[ V = \text{Length} \times \text{Width} \times \text{Height} \][/tex]
Plugging in the given dimensions:
[tex]\[ V = 3.00 \text{ cm} \times 3.00 \text{ cm} \times 3.00 \text{ cm} \][/tex]
[tex]\[ V = 27.0 \text{ cm}^3 \][/tex]
2. Understand the relationship between the block and the water:
When the block sinks completely in water, it displaces a volume of water equal to the volume of the block itself.
3. Determine the volume of water displaced:
Since the block displaces water equal to its own volume, the volume of water displaced is:
[tex]\[ \text{Volume of water displaced} = \text{Volume of iron block} \][/tex]
[tex]\[ \text{Volume of water displaced} = 27.0 \text{ cm}^3 \][/tex]
Therefore, the volume of water displaced by the block of iron is:
[tex]\[ \boxed{27.0 \text{ cm}^3} \][/tex]
This matches the given multiple-choice answer of [tex]\( 27.0 \text{ cm}^3 \)[/tex].
1. Calculate the volume of the iron block using its dimensions:
The block's dimensions are:
[tex]\[ \text{Length} = 3.00 \text{ cm} \][/tex]
[tex]\[ \text{Width} = 3.00 \text{ cm} \][/tex]
[tex]\[ \text{Height} = 3.00 \text{ cm} \][/tex]
The formula for the volume [tex]\( V \)[/tex] of a rectangular block is:
[tex]\[ V = \text{Length} \times \text{Width} \times \text{Height} \][/tex]
Plugging in the given dimensions:
[tex]\[ V = 3.00 \text{ cm} \times 3.00 \text{ cm} \times 3.00 \text{ cm} \][/tex]
[tex]\[ V = 27.0 \text{ cm}^3 \][/tex]
2. Understand the relationship between the block and the water:
When the block sinks completely in water, it displaces a volume of water equal to the volume of the block itself.
3. Determine the volume of water displaced:
Since the block displaces water equal to its own volume, the volume of water displaced is:
[tex]\[ \text{Volume of water displaced} = \text{Volume of iron block} \][/tex]
[tex]\[ \text{Volume of water displaced} = 27.0 \text{ cm}^3 \][/tex]
Therefore, the volume of water displaced by the block of iron is:
[tex]\[ \boxed{27.0 \text{ cm}^3} \][/tex]
This matches the given multiple-choice answer of [tex]\( 27.0 \text{ cm}^3 \)[/tex].
