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.
You have to find 1/3 of 24, so it is 8
She can make 9 bracelets
I found this by dividing the two numbers
Hope this helps
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Since A (3,4) A’(9,12)
You can see 3*3=9
Therefor it was enlarged by 3times
Scale factor of 3
-5(2x+1)-2x-2=17
first, distribute
-10x-5-2x-2=17
combine like terms
-12x-7=17
get the x alone, eliminate the constant
-12x=24
divide out the -12 to get the x alone.
x=-2
