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
_____
<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.
Answer:
110 in³
Step-by-step explanation:
The volume of a rectangular prism is the product of its dimensions:
V = LWH
V = (10 in)(2 in)(5.5 in) = 110 in³
Answer:f
−
1
(
x
Step-by-step explanation:
Answer:
<h3>
= -1 </h3><h3>
*
= 1.4142</h3><h3>
= π =3.14159</h3><h3>
= π² = 9.8696</h3>
Explanation:
1.) Rewrite √24 = 
Rewrite √54 =
Divide both terms by the denominator; √6 cancels. 2-3 = -1
2.) Rewrite as 
×
The 3's cancel. 10/2 = 5√2 in the numerator.
√5 × √5 = 5 in the denominator. The 5's cancel.
That leaves √2 ≈1.4142
3.) Divide the terms in the numerator by the term in the denominator.
√2's cancel. 10π/2 = 5π 8π/2 = 4π
Subtract and we are left with π = 3.14159
4.) The square roots are reciprocals. They multiply to 1
We are left with π × π = π² ≈ 9.8696
<h3>
</h3>
Answer: 6 cups of milk
Step-by-step explanation:
1 cup =10 cookies
60 cookies divided 10 cookies= 6cups
