Question

mathematical connections in exercises 11 and 12, find the dimensions of the cube. check your answer. 11. volume = 64 in.³ cube diagram with side length labeled s 12. volume = 216 cm³ cube diagram with side length labeled s

Explanation:

Exercise 11:

Step1: Recall cube volume formula

The volume \( V \) of a cube with side length \( s \) is given by \( V = s^3 \). We know \( V = 64 \, \text{in}^3 \), so we set up the equation \( s^3 = 64 \).

Step2: Solve for \( s \)

To find \( s \), we take the cube root of both sides. \( s=\sqrt[3]{64} \). Since \( 4\times4\times4 = 64 \), \( \sqrt[3]{64}=4 \).

Step3: Check the answer

Substitute \( s = 4 \) back into the volume formula: \( V=4^3=64 \, \text{in}^3 \), which matches the given volume.

Step1: Recall cube volume formula

The volume \( V \) of a cube with side length \( s \) is \( V = s^3 \). Here, \( V = 216 \, \text{cm}^3 \), so \( s^3 = 216 \).

Step2: Solve for \( s \)

Take the cube root of both sides: \( s=\sqrt[3]{216} \). Since \( 6\times6\times6 = 216 \), \( \sqrt[3]{216}=6 \).

Step3: Check the answer

Substitute \( s = 6 \) into the volume formula: \( V = 6^3=216 \, \text{cm}^3 \), which matches the given volume.

Answer:

The side length of the cube is \( 4 \) inches.

Exercise 12: