Question:
Use the formulas below to find the surface area and volume of the cube, sphere, and cylinder “ice cubes”.
“Ice cube” measurements:
• Cube: s = 3 cm
• Sphere: r = 1 cm
• Cylinder: r = 2 cm and h= 3 cm
Note: After you find the surface area and volume of each shape, divide the surface area by the volume to find the surface area to volume ratio expressed as a single number. This should go in the last column.
Answer:
Cube:
Surface area = [tex]6s^2[/tex]
Surface area = 6 (3)(3)
Surface area = [tex]54 cm^2[/tex]
Volume = [tex]s^3[/tex]
Volume =[tex](3)^3[/tex]
Volume =[tex]27 cm^3[/tex]
Surface Area to Volume Ratio = [tex]\frac{54}{27}[/tex] = [tex]\frac{2}{1}[/tex] = 2:1
Sphere:
Surface area = [tex]4\pi r^2[/tex]
Surface area = [tex]4 \pi (1)(1)[/tex]
Surface area = [tex]12.566cm^2[/tex]
Surface area = [tex]13 cm^2[/tex] (rounding off )
Volume = [tex]\frac{4}{3} \pi r^3[/tex]
Volume =[tex]\frac{4}{3} \pi (1)^3[/tex]
Volume =[tex]4.188 cm^3[/tex]
Volume = [tex]4 cm^3[/tex] (rounding off )
Surface Area to Volume Ratio =[tex]\frac{13}{4}[/tex] = 13 : 1
Cylinder:
Surface Area [tex]= 2\pi r^2 + 2 \pi rh[/tex]
Surface Area = [tex]2\pi (2)^2 + 2 \pi (2)(3)[/tex]
Surface Area = [tex]2\pi (4) + 2 \pi (6)[/tex]
Surface Area = [tex]8 \pi + 12 \pi[/tex]
Surface Area = [tex]20 \pi[/tex]
Surface Area = [tex]62.83 cm^2[/tex]
Surface area = 63 [tex]cm^2[/tex] (rounding off )
Volume = [tex]\pi r^2 h[/tex]
Volume = [tex]\pi (2)^2 (3)[/tex]
Volume = [tex]\pi (4) (3)[/tex]
Volume = [tex]12 \pi[/tex]
Volume = 37 .699
Volume = 38 [tex]cm^3[/tex]
Surface Area to Volume Ratio = [tex]\frac{63}{38}[/tex] = 68 : 38
