Sphere slices

Calculate the volume and surface area of a sphere if two parallel circular cross-sections have radii r₁ = 32 cm and r₂ = 47 cm, and the distance between them is v = 21 cm.

Final Answer:

V =  530.8 dm³
S =  317 dm²

Step-by-step explanation:

$$\begin{gathered} r_1=32\text{cm} \\ {r}_2=47\text{cm} \\ v=21\text{cm} \\ {v}_2=\frac{|r_1^2-r_2^2+v^2|}{2\cdot v}=\frac{|32^2-47^2+21^2|}{2\cdot 21}=\frac{124}{7}\doteq 17.7143\text{cm} \\ r=\sqrt{r_2^2+v_2^2}=\sqrt{47^2+17.7143^2}\doteq 50.2274\text{cm} \\ {V}_1=\frac{4}{3}\cdot \pi \cdot r^3=\frac{4}{3}\cdot 3.1416\cdot 50.2274^3\doteq 530776.6252{\text{cm}}^3 \\ V=V_1\to {\text{dm}}^3=V_1:1000{\text{dm}}^3=530776.6252:1000{\text{dm}}^3=530.8{\text{dm}}^3=530.8{\text{dm}}^3 \end{gathered}$$

$$\begin{gathered} S_1=4\pi \cdot r^2=4\cdot 3.1416\cdot 50.2274^2\doteq 31702.3885 \\ S=S_1\to {\text{dm}}^2=S_1:100{\text{dm}}^2=31702.3885:100{\text{dm}}^2=317{\text{dm}}^2=317{\text{dm}}^2 \end{gathered}$$

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