Respuesta :
Answer:
Side = 3 cm
Step-by-step explanation:
Given:
[tex]\text{Volume of cube} = 27 \ \text{cm}^{3}[/tex]
The formula to calculate the volume is (Side)³.
Thus, we obtained the following equation:
[tex](\text{Side})^{3} = 27 \text{cm}^{3} \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [\text{Side}^{3} = \text{Volume of cube}][/tex]
Cube root both sides to obtain the side length of the cube:
[tex]\implies \sqrt[3]{\text{(Side)}^{3}} = \sqrt[3]{27 \ \text{cm}^{3} }[/tex]
Evaluate the side of the cube:
[tex]\implies \sqrt[3]{\text{(Side)}^{3}} = \sqrt[3]{27 \ \text{cm}^{3} }[/tex]
[tex]\implies \sqrt[3]{\text{(Side)}\text{(Side)(Side})} = \sqrt[3]{3 \times 3 \times 3 \times \text{(cm)(cm)(cm)}}[/tex]
[tex]\implies \text{Side = 3 cm}[/tex]
Answer:
3 cm
Step-by-step explanation:
Formula
Volume of a cube = [tex]a^3[/tex] (where a is the side length)
Given that the volume of the cube is 27 cm³, to find the side length, substitute the given volume into the equation and solve for [tex]a[/tex]:
[tex]\implies 27\: \sf cm^3=a^3[/tex]
Cube root both sides:
[tex]\implies \sqrt[3]{27\: \sf cm^3} =\sqrt[3]{a^3}[/tex]
[tex]\implies \sqrt[3]{27}\sqrt[3]{\sf cm^3} =\sqrt[3]{a^3}[/tex]
[tex]\implies 3\: \sf cm=a[/tex]
[tex]\implies a=3\: \sf cm[/tex]
Therefore, the length of each side of the cube is 3 cm.
