MO SK/CZ Z9–I–3

John had the ball that rolled into the pool, and it swam in the water. Its highest point was 2 cm above the surface. The diameter of the circle that marked the water level on the surface of the ball was 8 cm. Find the diameter of John ball.

Correct result:

D =  10 cm

Solution:

$$\begin{gathered} r^2=(8\mathrm{/}2{)}^2+(r-2{)}^2 \\ {r}^2=16+r^2-4r+4 \\ 0=20-4r \\ r=20\mathrm{/}4=5\text{ cm } \\ D=2\cdot r=2\cdot 5=10\text{ cm} \end{gathered}$$

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Math student

I need more explanation as to where these equations are coming from.

3 years ago  Like

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