What is the volume of the largest right circular cone that can be inscribed in a sphere of radius r?
πR3 cubic units
Summary: 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 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.
| Algebra | Structural Analysis |
|---|---|
| Differential Calculus | Timber Design |
| Integral Calculus | Fluid Mechanics and Hydraulics |
How do you find the height of a right circular cone?
FAQs on Cone Height Formula The height of the cone using cone height formulas are, h = 3V/πr 2 and h = √l2 – r2, where V = Volume of the cone, r = Radius of the cone, and l = Slant height of the cone.
What is the volume of the largest cone that can be inscribed?
Answer: Required volume of largest cone is 359.34 cm³.
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 largest right circular cone?
The volume of the largest right circular cone that can be cut out from a cube of edge 4.2 cm is 19.404 cm^3. Hence, the volume of the largest right circular cone that can be cut out from a cube of edge 4.2 cm is 19.404 cm^3.
What is the volume of the largest cone that can be?
What is a right circular cone?
a cone whose surface is generated by lines joining a fixed point to the points of a circle, the fixed point lying on a perpendicular through the center of the circle.
What is the height of a circular cone the area of that cone is equal?
Hence, the height of the cone cannot be determined. Correct answer is (D)….Discussion :: Volume and Surface Area – Data Sufficiency 1 (Q. No. 4)
| What is the height of a circular cone? | |
|---|---|
| I. | The area of that cone is equal to the area of a rectangle whose length is 33 cm. |
| II. | The area of the base of that cone is 154 sq. cm. |
What is the volume equation of a cone?
The formula for the volume of a cone is V=1/3hπr². Learn how to use this formula to solve an example problem.
How do you find the maximal volume of a cone?
Finding the maximal volume is a simple algebra problem now. With given radius r of a sphere let the inscribed cone have height h then remaining length without radius is (h-r) let R be radius of cone then there we get a right angle triangle with r as hypotanious R as adjecent and (h-r) as opposite side.
How do you find the length of a cone with radius r?
With given radius r of a sphere let the inscribed cone have height h then remaining length without radius is (h-r) let R be radius of cone then there we get a right angle triangle with r as hypotanious R as adjecent and (h-r) as opposite side. Now by pythagorus theorem ((h-r)^2)+(R^2)=(r^2).
How do you find the volume of an inscribed cylinder?
Let x be the radius of the cylinder and y be the distance from the top of the cone to the top of the inscribed cylinder. Therefore, the height of the cylinder is h – y The volume of the inscribed cylinder is V = πx^2 (h-y) . We use the method of similar ratios to find a relationship between the height and radius, h-y and x .
How do you find the radius of the base of a sphere?
The height h is the distance from the apex to the circular base. It is between 0 and 2 r (with r the radius of the sphere), and the radius of the base grows as h increases from 0 to r and then shrinks again as h increases to 2 r. A diagram may convince you that by Pythagoras ( h − r) 2 + x 2 = r 2, where x is the radius of the base.