Answer:
1296√3 cubic units
Step-by-step explanation:
The volume of the prism will be the product of its base area and its height. Since it circumscribes a sphere with diameter 12, that is the height of the prism.
The central cross section of the sphere is a circle of radius 6, and that will be the size of the incircle of the base. That is, the base will have an altitude of 3 times that incircle radius, and an edge length of 2√3 times that incircle radius. Hence the area of the triangular base is ...
B = (1/2)(6×2√3)(6×3) = 108√3 . . . . . square units
The volume of the prism is then ...
V = Bh = (108√3)(12) = 1296√3 . . . cubic units
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<em>Comment on the geometry</em>
The centroid of an equilateral triangle is also the incenter and the circumcenter. The distance of that center from any edge of the triangle is 1/3 the height of the triangle. So, for an inradius of 6, the triangle height is 3×6 = 18. The side length of an equilateral triangle is 2/√3 times the altitude, so is 12√3 units for this triangle.
10.7%
possibility to get a blue marker : 4/15
possibility to get a green marker: 6/15
possibility to get a blue then a green: 24/225
= 10.666666%
= 10.7%
Answer:
£4.50
Step-by-step explanation:
She is at the car park for 2 hours and 30 minutes.
It would be £4.50 because 2 hours and 30 minutes is between 2-4 hours.
It can't be £3.00 because it would be too little time (2 hours or less) and it wouldn't be £5.50 because she would be paying for more time than she was there for (5 hours or more).
Hope this helps :)