On the circular 3

On the circular cap of a salt shaker with a diameter of 4.5 cm there are two types of holes. On the left is a semicircular hole with a diameter of 2.4 cm, on the right are five small circular holes with a diameter of 3 millimeters. Determine the ratio of the areas of the holes on the left and right sides of the cap.

Correct answer:

x =  32:5

Step-by-step explanation:

$$\begin{gathered} d_1=2.4\text{cm} \\ {d}_2=3\text{mm}\to \text{cm}=3:10\text{cm}=0.3\text{cm} \\ {n}_2=5 \\ {r}_1=d_1/2=2.4/2=\frac{6}{5}=1\frac{1}{5}=1.2\text{cm} \\ {S}_1=\pi \cdot r_1^2/2=3.1416\cdot 1.2^2/2\doteq 2.2619{\text{cm}}^2 \\ {r}_2=d_2/2=0.3/2=\frac{3}{20}=0.15\text{cm} \\ {S}_2=n_2\pi \cdot r_2^2=5\cdot 3.1416\cdot 0.15^2\doteq 0.3534{\text{cm}}^2 \\ x=S_1/S_2=2.2619/0.3534=6.4=32:5 \end{gathered}$$

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