What is the volume of largest cylinder that can be inscribed in a sphere?
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What is the volume of largest cylinder that can be inscribed in a sphere?
Let R be the radius and h be the height of the cylinder which is inscribed in a sphere of radius r cm. Let V be the volume of the cylinder. = π × 2 r 2 3 × 2 r 3 = 4 π r 3 3 3 cu cm. Hence, the volume of the largest cylinder inscribed in a sphere of radius ‘r’ cm = 4 r 3 3 3 cu cm.
How do you find the greatest volume of a cylinder?
We subtract 𝑟 squared from both sides. And dividing through by 𝑟, we find ℎ in terms of 𝑟: ℎ equals 12 minus 𝑟 squared over 𝑟. We substitute this expression for ℎ in terms of 𝑟 into the formula for the volume of 𝑉. We now have 𝑉 as a function of 𝑟: 𝑉 equals 𝜋𝑟 squared times 12 minus 𝑟 squared over 𝑟.
Which is bigger cylinder or sphere?
(Answer: The sphere takes up two-thirds of the volume of the cylinder.)
What is the cylinder that can be fitted in a sphere of given radius r?
Let R be the radius of the sphere and let h be the height of the cylinder centered on the center of the sphere. By the Pythagorean theorem, the radius of the cylinder is given by r2=R2−(h2)2. The volume of the cylinder is hence V=πr2h=π(hR2−h34).
How many spheres can fit in a cylinder?
There can be five sphere can be made from cylinder.
What is the difference between cylinder and sphere?
A cylinder is similar to a prism, but its two bases are circles, not polygons. Also, the sides of a cylinder are curved, not flat. A cone has one circular base and a vertex that is not on the base. The sphere is a space figure having all its points an equal distance from the center point.
How are the volumes of cylinders cones and spheres related?
The formula for the volume of a sphere is 4⁄3πr³. For a cylinder, the formula is πr²h. A cone is ⅓ the volume of a cylinder, or 1⁄3πr²h. This song’s hook makes these formulas easy to remember.
What is the volume of a box that can be inscribed in a sphere of unit radius?
Summary: The maximal volume of the rectangle inside the sphere of radius r and that volume is 8r3/3√3.
What is the ratio of the radii of the sphere and the cylinder?
Answer: The ratio of the radii of two spheres is 1:2. The two spheres are melted together to form a cylinder of height which is 12 times its radius.
Why is a sphere volume 4 3?
Volume of a sphere = 4/3 πr3 If you consider a circle and a sphere, both are round. The difference between the two shapes is that a circle is a two-dimensional shape and a sphere is a three-dimensional shape which is the reason that we can measure the Volume and area of a Sphere.
Why is a spheres volume 4 3?
What part of a cylinder is a single sphere?
You could also think of a cylinder as a “circular prism”. consists of two congruent, parallel circles joined by a curved surface. A cone is a three-dimensional solid that has a circular base joined to a single point (called the vertex) by a curved side….Surface Area of a Cone.
| s 2 | = | + × π |
|---|---|---|
| s | = | + × |
Why volume of cylinder is πr2h derived it?
Thus, the volume of the cylinder can be given by the product of the area of base and height. For any cylinder with base radius ‘r’, and height ‘h’, the volume will be base times the height. Therefore, the volume of a cylinder = πr2h cubic units.
