Hemisphere layer

Find the volume of the spherical layer that results from a hemisphere with a radius of 5 cm by cutting a paragraph whose height is 1.5 cm.

Correct answer:

V =  158.6286 cm³

Step-by-step explanation:

$$\begin{gathered} r=5\text{cm} \\ h=1.5\text{cm} \\ {V}_1=\frac{1}{6}\cdot \pi \cdot h^2\cdot (3\cdot r-h)=\frac{1}{6}\cdot 3.1416\cdot 1.5^2\cdot (3\cdot 5-1.5)\doteq 15.9043{\text{cm}}^3 \\ {V}_2=\frac{4}{3}\cdot \frac{1}{3}\cdot \pi \cdot r^3=\frac{4}{3}\cdot \frac{1}{3}\cdot 3.1416\cdot 5^3\doteq 174.5329{\text{cm}}^3 \\ V=V_2-V_1=174.5329-15.9043=158.6286{\text{cm}}^3 \end{gathered}$$

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