4. If the total surface area of a cube is 216 cm2, then find its volume.

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Finding the Volume of a Cube Understanding the Problem To find the volume of a cube, we first need to understand the given information: Total surface area of the cube is 216 cm². Solution Steps Determine the Side Length of the Cube Since a cube has six equal square faces, the total surface...
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Finding the Volume of a Cube Understanding the Problem To find the volume of a cube, we first need to understand the given information: Total surface area of the cube is 216 cm². Solution Steps Determine the Side Length of the Cube Since a cube has six equal square faces, the total surface area can be expressed as 6s26s2, where ss is the side length of the cube. So, 6s2=216 cm26s2=216cm2. Solving for ss, we get s=2166s=6216 . Calculate the Volume of the Cube Once we have the side length, we can calculate the volume of the cube using the formula V=s3V=s3. Substituting the value of ss, we get V=(2166)3V=(6216 )3. Simplify to find the volume. Detailed Calculation Determine the Side Length of the Cube Given: Total surface area (AA) = 216 cm². Formula for total surface area: A=6s2A=6s2. Substitute the given value: 216=6s2216=6s2. Solve for ss: s=2166s=6216 . Calculate: s=36s=36 . Thus, s=6 cms=6cm. Calculate the Volume of the Cube Formula for volume: V=s3V=s3. Substitute the value of ss: V=63V=63. Calculate: V=216 cm3V=216cm3. Final Answer The volume of the cube is 216 cm3216cm3. read less
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