Cell Structure And Functioncell The Unit Of Life Topic

NEET & Advance Numericals#

1. If a cell has a surface area of $100 µm^2$ and a membrane thickness of $10 nm$, what is the volume of the membrane in cubic micrometers $(µm^3)$?

Solution:

Using the formula: $V = A × t$, where $V$ is the volume, $A$ is the surface area, and $t$ is the thickness, we get:

$V = 100 µm^2 × 10 nm = 1000 nm·µm^2$

Therefore, the volume of the membrane is $1000 , \mu m^3$.

2. A cell has a diameter of $10 µm$. What is the approximate surface area of the cell in $µm^2$?

Solution:

Using the formula for the surface area of a sphere, $A = 4πr^2$, where $A$ is the surface area and $r$ is the radius, and assuming the cell is spherical, we get:

$r = 10 µm / 2 = 5 µm$. $A = 4π × (5 µm)^2 ≈ 314 µm^2$.

Therefore, the approximate surface area of the cell is $314 µm^2$.

3. A cell has a volume of $1000 µm^3$. What is the approximate diameter of the cell in $µm$?

Solution:

Using the formula for the volume of a sphere, $V = 4/3πr^3$, where $V$ is the volume and $r$ is the radius, and assuming the cell is spherical, we can solve for $r$:

$r^3 = V / (4/3π) = (1000 µm^3) / (4/3 × 3.14) ≈ 238.7 µm^3$ $r ≈ ∛244 µm^3 ≈ 6 µm$.

Therefore, the approximate diameter of the cell is $12 µm$.

CBSE Board Numericals#

A plant cell has a surface area of $100 µm^2$ and a membrane thickness of $10 nm$. Calculate the surface area-to-volume ratio of the cell.

Solution:

Using the formula for surface area-to-volume ratio, $SA:V = A / V$, where $SA:V$ is the surface area-to-volume ratio, $A$ is the surface area, and $V$ is the volume, we get:

$SA: V = 100 µm^2 / 1000 µm^3 = 0.1 µm^2/µm^3$.

Therefore, the surface area-to-volume ratio of the cell membrane is $0.1 µm^{-1}$.

2. A human red blood cell has a diameter of $8 µm$. What is the volume of a single red blood cell in $µm^3$?

Solution:

Using the formula for the volume of a sphere, $V = \frac{4}{3}πr^3$, where $V$ is the volume and $r$ is the radius, and assuming the red blood cell is spherical, we get:

$r = 8 µm / 2 = 4 µm$. $V = 4/3π × (4 µm)^3 ≈ 268 µm^3$.

Therefore, the volume of a single red blood cell is approximately $90 µm^3$.

3. A typical plant cell has a surface area-to-volume ratio of $4:1$. If the surface area of the cell is $1000 µm^2$, what is the volume of the cell in $µm^3$?

Solution:

Rearranging the formula $SA: V = A/V$ to $SA: V = A/V$, where $V$ is the volume, $A$ is the surface area, and $SA: V$ is the surface area-to-volume ratio, and substituting the given values, we get:

$V = 1000 µm^2 / 4 µm^2/µm^3 = 250 µm^3$.

Therefore, the volume of the cell is $250 µm^3$.