Spherical 83427

The bowl, in the shape of part of a spherical surface, has a diameter of 28 cm at the top edge and is 8 cm deep. What is the total volume of the bowl? How much water would you have to pour into the bowl to fill it halfway?

Correct answer:

V =  2278.7019 cm³
V₂ =  636.6961 cm³

Step-by-step explanation:

$$\begin{gathered} d=28\text{cm} \\ v=8\text{cm} \\ r=d/2=28/2=14\text{cm} \\ V=\pi \cdot v^2\cdot (r-\frac{v}{3})=3.1416\cdot 8^2\cdot (14-\frac{8}{3})=2278.7019{\text{cm}}^3 \end{gathered}$$

$$\begin{gathered} v_2=v/2=8/2=4\text{cm} \\ {V}_2=\pi \cdot v_2^2\cdot (r-\frac{v_2}{3})=3.1416\cdot 4^2\cdot (14-\frac{4}{3})=636.6961{\text{cm}}^3 \end{gathered}$$

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