Two Sections

A sphere with a radius of 5 cm was divided into two spherical caps. The height of the smaller cap is 1 cm. Determine the volume of the smaller cap to the nearest hundredth of a cm³.

Final Answer:

V₂ =  14.66 cm

Step-by-step explanation:

$$\begin{gathered} r=5\text{cm} \\ {v}_1=1\text{cm} \\ {v}_2=2\cdot r-v_1=2\cdot 5-1=9\text{cm} \\ {v}_1<v_2 \\ {V}_2=V_1=\frac{\pi \cdot v_1^2}{3}\cdot (3\cdot r-v_1)=\frac{3.1416\cdot 1^2}{3}\cdot (3\cdot 5-1)=14.66\text{cm} \end{gathered}$$

Try another example