The side length is the cube root of 460.
cube root(460) = 460^(1/3)
That's approximately 7.7
Answer:
Multiples of 120 are 120, 240, 360, 480, 600, 720, 840 etc; Multiples of 150 are 150, 300, 450, 600, 750, 900 etc; Therefore, the least common multiple of 120 and 150 is 600.
Least common multiple (LCM) of 19600 and 19619 is 384532400.
Wrong , actually the complement of an obtuse angle is a right angle
yw brodie
<span>S = 2Πrh + 2Πr2
Manipulating the equation for h.
Step 1. subtract </span><span>2Πr2 on both sides.
</span>S - 2Πr2 = 2Πrh + 2Πr2 - 2Πr2
S - 2Πr2 = <span>2Πrh
</span>
Step 2 . divide <span>2Πr on both sides
</span>
(S - 2Πr2)/2Πr = 2Πrh/<span>2Πr
</span><span>h = </span>(S - 2Πr2)/2Πr
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.