A rectangular parallelepiped is circumscribed about a cylinder whose base radius is 5
| June 15, 2021 | education
A rectangular parallelepiped is circumscribed about a cylinder whose base radius is 5. The height of the cylinder is 7. Find the volume of the parallelepiped.
Since a rectangular parallelepiped is circumscribed around a cylinder, the base of this cylinder is a circle inscribed in the base of this parallelepiped.
Thus, the base of a rectangular parallelepiped is a square, the side of which is equal to the diameter of the circle.
Therefore, the area of the base of the rectangular parallelepiped is:
S = (5 + 5) ² = 100.
Since the height of the cylinder is equal to the height of the parallelepiped described around it, the volume of the parallelepiped will be equal to:
V = 100 * 7 = 700.
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