Math Snap

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.$$Density\, of\, cube > Density\, of\, water$$

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.