Hemisphere cut

Calculate the spherical layer's volume that remains from the hemisphere after the 3 cm section is cut. The height of the hemisphere is 10 cm.

Correct answer:

V =  1839.9261 cm³

Step-by-step explanation:

$$\begin{gathered} v=3\text{cm} \\ r=10\text{cm} \\ {V}_1=\frac{4}{3}\cdot \pi \cdot r^3=\frac{4}{3}\cdot 3.1416\cdot 10^3\doteq 4188.7902{\text{cm}}^3 \\ {V}_2=\frac{1}{3}\cdot \pi \cdot v^2\cdot (3\cdot r-v)=\frac{1}{3}\cdot 3.1416\cdot 3^2\cdot (3\cdot 10-3)\doteq 254.469{\text{cm}}^3 \\ V=V_1/2-V_2=4188.7902/2-254.469=1839.9261{\text{cm}}^3 \end{gathered}$$

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