Question

Pre Algebra

Answer 1

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 =  $6s^2$

Surface area  =  6 (3)(3)

Surface area =  $54 cm^2$

Volume =  $s^3$

Volume  =$(3)^3$

Volume  =$27 cm^3$

Surface Area to Volume Ratio = $\frac{54}{27}$ = $\frac{2}{1}$ = 2:1

Sphere:

Surface area =  $4\pi r^2$

Surface area  =  $4 \pi (1)(1)$

Surface area =  $12.566cm^2$

Surface area =  $13 cm^2$ (rounding off )

Volume =  $\frac{4}{3} \pi r^3$

Volume  =$\frac{4}{3} \pi (1)^3$

Volume  =$4.188 cm^3$

Volume  = $4 cm^3$ (rounding off )

Surface Area to Volume Ratio =$\frac{13}{4}$ = 13  : 1

Cylinder:

Surface Area $= 2\pi r^2 + 2 \pi rh$

Surface Area  =  $2\pi (2)^2 + 2 \pi (2)(3)$

Surface Area  =  $2\pi (4) + 2 \pi (6)$

Surface Area  =  $8 \pi + 12 \pi$

Surface Area =  $20 \pi$

Surface Area  =  $62.83 cm^2$

Surface area = 63 $cm^2$ (rounding off )

Volume  =  $\pi r^2 h$

Volume   = $\pi (2)^2 (3)$

Volume  =  $\pi (4) (3)$

Volume  = $12 \pi$

Volume  =  37 .699

Volume  =  38 $cm^3$

Surface Area to Volume Ratio = $\frac{63}{38}$  =  68 : 38