The sides of the base of the rectangular parallelepiped are 3 cm and 4 cm, the side edge is 12 cm.
| February 6, 2021 | education
The sides of the base of the rectangular parallelepiped are 3 cm and 4 cm, the side edge is 12 cm. Find the surface area of the described sphere.
In order to find the surface area of the described ball, we need to find its radius, the radius is half of the parallelepiped diagonal, then we denote the parallelepiped diagonal as C1A, the base diagonal as AC, the side edge of CC1. C1A, AC and CC1 are the sides of a right-angled triangle, so we can find C1A.
AC = √3 ^ 2 + 4 ^ 2 = √25 = 5 cm.
CC1 = 12 cm.
C1A = √12 ^ 2 + 5 ^ 2 = 13 cm.
We got that the diameter of the described ball is 13 cm, then the radius is 6.5 cm.
Ball surface area:
S = 4 * R ^ 2 * π = 4 * (6.5) ^ 2 * π = 169π cm2.
Answer: 169π cm2.
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