Question

measure the surface area and the volume of each of the cubes below. show your work!
1 cm 2 cm 3 cm
box 1 box 2 box 3
surface area
volume
sa/ratio

Explanation:

Step1: Calculate surface area of cube

The formula for the surface area (\(SA\)) of a cube is \(SA = 6s^{2}\), where \(s\) is the side - length.

• For Box 1 (\(s = 1\) cm): \(SA_1=6\times(1)^{2}=6\) \(cm^{2}\)
• For Box 2 (\(s = 2\) cm): \(SA_2 = 6\times(2)^{2}=6\times4 = 24\) \(cm^{2}\)
• For Box 3 (\(s = 3\) cm): \(SA_3=6\times(3)^{2}=6\times9 = 54\) \(cm^{2}\)

Step2: Calculate volume of cube

The formula for the volume (\(V\)) of a cube is \(V=s^{3}\).

• For Box 1 (\(s = 1\) cm): \(V_1=(1)^{3}=1\) \(cm^{3}\)
• For Box 2 (\(s = 2\) cm): \(V_2=(2)^{3}=8\) \(cm^{3}\)
• For Box 3 (\(s = 3\) cm): \(V_3=(3)^{3}=27\) \(cm^{3}\)

Step3: Calculate SA/Volume ratio

The ratio \(\frac{SA}{V}=\frac{6s^{2}}{s^{3}}=\frac{6}{s}\)

• For Box 1 (\(s = 1\) cm): \(\frac{SA_1}{V_1}=\frac{6}{1}=6\)
• For Box 2 (\(s = 2\) cm): \(\frac{SA_2}{V_2}=\frac{24}{8}=3\)
• For Box 3 (\(s = 3\) cm): \(\frac{SA_3}{V_3}=\frac{54}{27}=2\)

Answer:

	Box 1	Box 2	Box 3
Volume (\(cm^{3}\))	\(1\)	\(8\)	\(27\)
SA/Volume Ratio	\(6\)	\(3\)	\(2\)