Question

During concretionary growth of a spherical grain of radius 2 Å, the rate of change of surface area with respect to change in radius of the grain is __________ ×10^–8 cm. (Use π = 3.14) (Round off to two decimal places.)

Hint:

Always convert Å → cm (1 Å = 10\textsuperscript{–8} cm) before substitution.

Answer 1

Correct Answer: 50.2

Step 1: Formula for rate of change.
For a sphere, \( A = 4 \pi r^{2} \). \[ \frac{dA}{dr} = 8 \pi r \] Step 2: Convert radius.
\( r = 2 \, \text{Å} = 2 \times 10^{-8} \, \text{cm}. \)
Step 3: Substitute.
\[ \frac{dA}{dr} = 8 \times 3.14 \times 2 \times 10^{-8} = 50.24 \times 10^{-8} \, \text{cm.} \] Step 4: Round off.
5.02 ×10^–7 cm = 5.02 ×10^–8 (in given format).