Paragraphs 69164

What is the volume of the spherical layer that remains after cutting the paragraphs on both sides of the ball, whose height is 3.5 cm? Is the diameter of the ball 24 cm?

Correct answer:

V =  6404.3984 cm³

Step-by-step explanation:

$$\begin{gathered} v=3.5\text{cm} \\ d=24\text{cm} \\ r=d/2=24/2=12\text{cm} \\ {V}_1=\frac{4}{3}\cdot \pi \cdot r^3=\frac{4}{3}\cdot 3.1416\cdot 12^3\doteq 7238.2295{\text{cm}}^3 \\ {V}_2=\frac{1}{3}\cdot \pi \cdot v^2\cdot (3\cdot r-v)=\frac{1}{3}\cdot 3.1416\cdot 3.5^2\cdot (3\cdot 12-3.5)\doteq 416.9155{\text{cm}}^3 \\ V=V_1-2\cdot V_2=7238.2295-2\cdot 416.9155=6404.3984{\text{cm}}^3 \end{gathered}$$

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