JEE Main & 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 µm^3.

Therefore, the volume of the membrane is 1000 µm^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) ≈ 244 µm^3. r ≈ ∛244 µm^3 ≈ 6 µm.

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

CBSE Board Numericals

1. 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 membrane.

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^2/µm^3.

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 = 4/3πr^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 268 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 V = A/SA, 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.