Find the area and the volume of a spherical area whose circumferences have radius $$10$$cm and $$8$$ cm, and the distance between them is $$5$$ cm.
See development and solution
Development:
From the formula of the calculation of the area and volume of a spherical area, we have :
$$$A=2\cdot\pi\cdot 10\cdot 5= 314,16 \text{ cm}^2$$$
$$$V=\dfrac{1}{6}\cdot \pi\cdot 5\cdot(5^2+3\cdot 10^2+3 \cdot 8^2)= 1353,5\text{ cm}^3$$$
Solution:
The area of the spherical area is $$314,16 \text{ cm}^2$$ and the volume is $$1353,5\text{ cm}^3$$.