Diameter of oil drop, d_drop = 0.05 cm

Question

ScanSolve AI Tutor · Accepted Answer

Here are the calculations for the oil drop experiment:

Given:
Diameter of oil drop, $d_{drop} = 0.05 \text{ cm}$
Diameter of circular patch, $d_{patch} = 20 \text{ cm}$

b) (i) The volume of the oil drop

Calculate the radius of the oil drop.
$r_{drop} = \frac{d_{drop}}{2}$ $r_{drop} = \frac{0.05 \text{ cm}}{2}$ $r_{drop} = 0.025 \text{ cm}$
Calculate the volume of the oil drop using the formula for the volume of a sphere.
$V_{drop} = \frac{4}{3} \pi r_{drop}^3$ $V_{drop} = \frac{4}{3} \pi (0.025 \text{ cm})^3$ $V_{drop} = \frac{4}{3} \pi (0.000015625 \text{ cm}^3)$ $V_{drop} \approx 6.54 \times 10^{-5} \text{ cm}^3$
The volume of the oil drop is \boxed{\text{6.54 \times 10^{-5} cm}^3}.

b) (ii) The area of the patch covered by the oil
Calculate the radius of the circular patch.
$r_{patch} = \frac{d_{patch}}{2}$ $r_{patch} = \frac{20 \text{ cm}}{2}$ $r_{patch} = 10 \text{ cm}$
Calculate the area of the patch using the formula for the area of a circle.
$A_{patch} = \pi r_{patch}^2$ $A_{patch} = \pi (10 \text{ cm})^2$ $A_{patch} = 100 \pi \text{ cm}^2$ $A_{patch} \approx 314.16 \text{ cm}^2$
The area of the patch covered by the oil is $\boxed{\text{314.16 cm}^2}$ .

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