How do you find the maximum volume of a cone inscribed a sphere?
Since it is a right circular cone then, r2 = R2 – x2 by Pythagoras theorem. Therefore, the volume of the largest right circular cone that can be inscribed in a sphere of the radius R is (32/81)πR3 cubic units or (8/27) times the volume of the sphere.
What is the volume of the largest cone that can be inscribed?
Answer: Required volume of largest cone is 359.34 cm³.
What is the circular cone of maximum volume inscribed in a sphere of a radius A?
Find the circular cone of maximum volume inscribed in a sphere of radius a. The sphere is given, thus radius a is constant….More Reviewers.
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What is the maximum volume of a cylinder inscribed in a sphere?
As it is clear from the figure below that the radius of the sphere = r cm, radius of the cylinder =R cm and the height of the cylinder = h cm. Hence, the volume of the largest cylinder that can be inscribed in a sphere of radius $3\sqrt 3 $ cm is $108 cm^3$.
What does it mean to be inscribed in a sphere?
In geometry, the inscribed sphere or insphere of a convex polyhedron is a sphere that is contained within the polyhedron and tangent to each of the polyhedron’s faces.
What is the volume of the sphere?
The formula for the volume of a sphere is V = 4/3 πr³.
What is the volume equation of a cone?
Now that you have what you need to calculate the volume of a cone, all you have to do is follow the formula : V = 1/3Bh, where B = πr². Now, you need to multiply the area of the base B by the height h and then divide the obtained result by 3.
What is the formula of CSA of cone?
The curved surface area of the cone can be given by finding the area of the sector by using the formula, Area of the sector (in terms of length of arc) = (arc length × radius)/ 2 = ((2πr) × l)/2 = πrl.
What is the maximum volume of cylinder?
Therefore the volume is a maximum when 2r−2h+h=0, so h=2r and hr=2. Let the ratio of height to radius be ρ, then h=ρr. The volume of the cylinder is V=πr2h=πρr3.
What figures can be inscribed in a circle?
Familiar examples of inscribed figures include circles inscribed in triangles or regular polygons, and triangles or regular polygons inscribed in circles. A circle inscribed in any polygon is called its incircle, in which case the polygon is said to be a tangential polygon.
Why is it 4 3 for volume of a sphere?
Since the cylinder/cone and hemisphere have the same height, by Cavalieri’s Principle the volumes of the two are equal. The cylinder volume is πR3, the cone is a third that, so the hemisphere volume is 23πR3. Thus the sphere of radius R has volume 43πR3.