Question

Estimate the surface area of a spherical nanoparticle with a diameter of 10 nm.

• A. 100nm\(^2\)
• B. 250nm\(^2\)
• C. 314nm\(^2\)
• D. 400nm\(^2\)

Hint:

Sphere Surface Area. \(A = 4 \pi r^2\), where r is the radius (r = diameter/2).

Answer 1

The Correct Option is C

Diameter (\(d\)) = 10 nm.
Radius (\(r\)) = Diameter / 2 = 10 nm / 2 = 5 nm.
The surface area (\(A\)) of a sphere is given by the formula: $$ A = 4 \pi r^2 $$ Substitute the radius: $$ A = 4 \pi (5 \, \text{nm})^2 = 4 \pi (25 \, \text{nm}^2) = 100 \pi \, \text{nm}^2 $$ Using the approximation \( \pi \approx (3)14 \): $$ A \approx 100 \times (3)14 \, \text{nm}^2 = 314 \, \text{nm}^2 $$ The surface area is approximately 314 nm\(^2\).