QuestionA cube with side $5.3 \mathrm{~cm}$ has a volume of $V$ and mass of 280g. Find density and determine if it floats in water.

Studdy Solution

STEP 1

Assumptions1. The side length of the cube is5.3 cm. The mass of the cube is280 grams3. The density of water is1 g/cm³

STEP 2

First, we need to find the volume of the cube. The formula for the volume of a cube is the side length cubed.
Volume = Side\, length^

STEP 3

Now, plug in the given value for the side length to calculate the volume.
$Volume = (5.3\, cm)^3$

STEP 4

Calculate the volume of the cube.
$Volume = (.3\, cm)^3 =148.877\, cm^3$

STEP 5

Now that we have the volume, we can find the density of the cube. The formula for density is mass divided by volume.
$Density = Mass / Volume$

STEP 6

Plug in the values for the mass and the volume to calculate the density.
$Density =280\, g /148.877\, cm^3$

STEP 7

Calculate the density of the cube.
$Density =280\, g /148.877\, cm^3 =1.88\, g/cm^3$

STEP 8

Now that we have the density of the cube, we can determine if it would float in water. A solid will float in water if its density is less than the density of water. $Density\, of\, cube > Density\, of\, water$

STEP 9

Plug in the values for the density of the cube and the density of water to determine if the cube would float.
$.88\, g/cm^3 >\, g/cm^3$ The cube would not float in water because its density is greater than g/cm³.

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QuestionA cube with side $5.3 \mathrm{~cm}$ has a volume of $V$ and mass of 280g. Find density and determine if it floats in water.

Studdy Solution

STEP 1

Assumptions1. The side length of the cube is5.3 cm. The mass of the cube is280 grams3. The density of water is1 g/cm³

STEP 2

First, we need to find the volume of the cube. The formula for the volume of a cube is the side length cubed.
Volume = Side\, length^

STEP 3

Now, plug in the given value for the side length to calculate the volume.
$Volume = (5.3\, cm)^3$

STEP 4

Calculate the volume of the cube.
$Volume = (.3\, cm)^3 =148.877\, cm^3$

STEP 5

Now that we have the volume, we can find the density of the cube. The formula for density is mass divided by volume.
$Density = Mass / Volume$

STEP 6

Plug in the values for the mass and the volume to calculate the density.
$Density =280\, g /148.877\, cm^3$

STEP 7

Calculate the density of the cube.
$Density =280\, g /148.877\, cm^3 =1.88\, g/cm^3$

STEP 8

Now that we have the density of the cube, we can determine if it would float in water. A solid will float in water if its density is less than the density of water. $Density\, of\, cube > Density\, of\, water$

STEP 9

Plug in the values for the density of the cube and the density of water to determine if the cube would float.
$.88\, g/cm^3 >\, g/cm^3$ The cube would not float in water because its density is greater than g/cm³.

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QuestionA cube with side 5.3 cm5.3 \mathrm{~cm}5.3 cm has a volume of VVV and mass of 280g. Find density and determine if it floats in water.

Studdy Solution

STEP 1

Assumptions1. The side length of the cube is5.3 cm. The mass of the cube is280 grams3. The density of water is1 g/cm³

STEP 2

First, we need to find the volume of the cube. The formula for the volume of a cube is the side length cubed.Volume = Side\, length^

STEP 3

Now, plug in the given value for the side length to calculate the volume.Volume=(5.3 cm)3Volume = (5.3\, cm)^3Volume=(5.3cm)3

STEP 4

Calculate the volume of the cube.Volume=(.3 cm)3=148.877 cm3Volume = (.3\, cm)^3 =148.877\, cm^3Volume=(.3cm)3=148.877cm3

STEP 5

Now that we have the volume, we can find the density of the cube. The formula for density is mass divided by volume.Density=Mass/VolumeDensity = Mass / VolumeDensity=Mass/Volume

STEP 6

Plug in the values for the mass and the volume to calculate the density.Density=280 g/148.877 cm3Density =280\, g /148.877\, cm^3Density=280g/148.877cm3

STEP 7

Calculate the density of the cube.Density=280 g/148.877 cm3=1.88 g/cm3Density =280\, g /148.877\, cm^3 =1.88\, g/cm^3Density=280g/148.877cm3=1.88g/cm3

STEP 8

Now that we have the density of the cube, we can determine if it would float in water. A solid will float in water if its density is less than the density of water.Density of cube>Density of waterDensity\, of\, cube > Density\, of\, waterDensityofcube>Densityofwater

STEP 9

Plug in the values for the density of the cube and the density of water to determine if the cube would float..88 g/cm3> g/cm3.88\, g/cm^3 >\, g/cm^3.88g/cm3>g/cm3The cube would not float in water because its density is greater than g/cm³.

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QuestionA cube with side $5.3 \mathrm{~cm}$ has a volume of $V$ and mass of 280g. Find density and determine if it floats in water.

First, we need to find the volume of the cube. The formula for the volume of a cube is the side length cubed.
Volume = Side\, length^

Now, plug in the given value for the side length to calculate the volume.
$Volume = (5.3\, cm)^3$

Calculate the volume of the cube.
$Volume = (.3\, cm)^3 =148.877\, cm^3$

Now that we have the volume, we can find the density of the cube. The formula for density is mass divided by volume.
$Density = Mass / Volume$

Plug in the values for the mass and the volume to calculate the density.
$Density =280\, g /148.877\, cm^3$

Calculate the density of the cube.
$Density =280\, g /148.877\, cm^3 =1.88\, g/cm^3$

Now that we have the density of the cube, we can determine if it would float in water. A solid will float in water if its density is less than the density of water. $Density\, of\, cube > Density\, of\, water$

Plug in the values for the density of the cube and the density of water to determine if the cube would float.
$.88\, g/cm^3 >\, g/cm^3$ The cube would not float in water because its density is greater than g/cm³.