2.3 Surface Area to Volume Ratios and Their Effects on Cells

Why is a high surface area to volume ratio beneficial for cells?

• It increases the cell's volume.

• It allows for more efficient material exchange.

• It decreases the cell's surface area.

• It makes the cell more rigid.

Answer explanation

A high surface area to volume ratio allows cells to efficiently exchange materials, such as nutrients and waste, with their environment. This is crucial for maintaining cellular functions and overall health.

Which type of cell would be most efficient in exchanging materials with its environment?

• A large cell with a low surface area to volume ratio.

• A small cell with a high surface area to volume ratio.

• A large cell with a high surface area to volume ratio.

• A small cell with a low surface area to volume ratio.

Answer explanation

A small cell with a high surface area to volume ratio is most efficient in exchanging materials because it maximizes the surface area available for diffusion relative to its volume, facilitating quicker and more effective material exchange.

Calculate the surface area of a sphere with a radius of 3 cm.

• \(36\pi \, \text{cm}^2\)

• \(27\pi \, \text{cm}^2\)

• \(9\pi \, \text{cm}^2\)

• \(18\pi \, \text{cm}^2\)

Answer explanation

The surface area of a sphere is calculated using the formula $4\pi r^2$. For a radius of 3 cm, the calculation is $4\pi (3^2) = 4\pi (9) = 36\pi \, \text{cm}^2$. Thus, the correct answer is $36\pi \, \text{cm}^2$.

Calculate the volume of a sphere with a radius of 3 cm.

• \(27\pi \, \text{cm}^3\)

• \(36\pi \, \text{cm}^3\)

• \(81\pi \, \text{cm}^3\)

• \(18\pi \, \text{cm}^3\)

Answer explanation

The volume of a sphere is calculated using the formula \(V = \frac{4}{3} \pi r^3\). For a radius of 3 cm, \(V = \frac{4}{3} \pi (3)^3 = \frac{4}{3} \pi (27) = 36\pi\, \text{cm}^3\). Thus, the correct answer is \(27\pi \, \text{cm}^3\).

Which of the following describes the relationship between surface area and volume as a cell increases in size?

• Surface area increases faster than volume.

• Volume increases faster than surface area.

• Surface area and volume increase at the same rate.

• Surface area decreases while volume increases.

Answer explanation

As a cell increases in size, its volume grows cubically (length^3), while surface area grows quadratically (length^2). Therefore, volume increases faster than surface area, making the correct choice: Volume increases faster than surface area.

Calculate the surface area of a cube with a side length of 4 cm.

• \(64 \, \text{cm}^2\)

• \(48 \, \text{cm}^2\)

• \(96 \, \text{cm}^2\)

• \(32 \, \text{cm}^2\)

Answer explanation

The surface area of a cube is calculated using the formula: 6 × (side length)². For a side length of 4 cm, the calculation is 6 × (4 cm)² = 6 × 16 cm² = 96 cm². Thus, the correct answer is 96 cm².

Calculate the volume of a cube with a side length of 4 cm.

• \(16 \, \text{cm}^3\)

• \(64 \, \text{cm}^3\)

• \(48 \, \text{cm}^3\)

• \(32 \, \text{cm}^3\)

Answer explanation

The volume of a cube is calculated using the formula V = side³. For a side length of 4 cm, V = 4³ = 64 cm³. Therefore, the correct answer is 64 cm³.

How do cells increase their surface area without significantly increasing their volume?

• By becoming spherical.

• By developing folds or microvilli.

• By dividing into smaller cells.

• By storing more water.

Answer explanation

Cells increase their surface area by developing folds or microvilli, which create more area for absorption and interaction without a significant increase in volume, unlike becoming spherical or dividing.

Calculate the surface area of a rectangular solid with dimensions 2 cm x 3 cm x 4 cm.

• \(52 \, \text{cm}^2\)

• \(24 \, \text{cm}^2\)

• \(48 \, \text{cm}^2\)

• \(36 \, \text{cm}^2\)

Answer explanation

The surface area of a rectangular solid is calculated using the formula: 2(lw + lh + wh). For dimensions 2 cm, 3 cm, and 4 cm, it equals 2(2*3 + 2*4 + 3*4) = 2(6 + 8 + 12) = 52 cm². Thus, the correct answer is 52 cm².

Calculate the volume of a rectangular solid with dimensions 2 cm x 3 cm x 4 cm.

• \(24 \, \text{cm}^3\)

• \(12 \, \text{cm}^3\)

• \(36 \, \text{cm}^3\)

• \(48 \, \text{cm}^3\)

Answer explanation

To find the volume of a rectangular solid, multiply the dimensions: 2 cm x 3 cm x 4 cm = 24 cm³. Therefore, the correct answer is 24 cm³.