Question

Compare the surface area to volume ratio of the below two objects: Which one will support the faster rate of diffusion?

Object A – Length = 3 cm, Height = 3 cm, Width = 8 cm
Object B – Length = 2 cm, Height = 9 cm, Width = 9 cm

a) Object A has a higher surface area to volume ratio and will support faster diffusion.
b) Object B has a higher surface area to volume ratio and will support faster diffusion.
c) Both objects have similar surface area to volume ratios.
d) It cannot be determined based on the given information.

Answer 1

Object A has a higher surface area to volume ratio and will support faster diffusion.

Step-by-step explanation:

The surface area to volume ratio is an important factor in determining the rate of diffusion. The surface area to volume ratio is calculated by dividing the surface area of an object by its volume. In this case, we need to compare the surface area to volume ratio of Object A and Object B.

Object A: Length = 3 cm, Height = 3 cm, Width = 8 cm

Surface Area of Object A = 2 * (Length * Width + Height * Width + Length * Height) = 2 * (3 * 8 + 3 * 8 + 3 * 3) = 2 * (24 + 24 + 9) = 2 * 57 = 114 square cm

Volume of Object A = Length * Height * Width = 3 * 3 * 8 = 72 cubic cm

Surface Area to Volume ratio of Object A = Surface Area / Volume = 114 / 72 = 1.5833

Object B: Length = 2 cm, Height = 9 cm, Width = 9 cm

Surface Area of Object B = 2 * (Length * Width + Height * Width + Length * Height) = 2 * (2 * 9 + 9 * 9 + 2 * 9) = 2 * (18 + 81 + 18) = 2 * 117 = 234 square cm

Volume of Object B = Length * Height * Width = 2 * 9 * 9 = 162 cubic cm

Surface Area to Volume ratio of Object B = Surface Area / Volume = 234 / 162 = 1.4444

Comparing the surface area to volume ratios of Object A and Object B, we can see that Object A has a higher surface area to volume ratio (1.5833) than Object B (1.4444). Therefore, Object A has a higher surface area to volume ratio and will support faster diffusion.