Advertisements
Advertisements
प्रश्न
A sphere is placed inside a right circular cylinder so as to touch the top, base and lateral surface of the cylinder. If the radius of the sphere is r, then the volume of the cylinder is
पर्याय
4πr3
`8/3 pi r^3`
2πr3
8πr3
Advertisements
उत्तर
In the given problem, we have a sphere inscribed in a cylinder such that it touches the top, base and the lateral surface of the cylinder. This means that the height and the diameter of the cylinder are equal to the diameter of the sphere.
So, if the radius of the sphere = r
The radius of the cylinder (rc)= r
The height of the cylinder (h) = 2r
Therefore, Volume of the cylinder = `pi r_c^2 h`
`= pi r^2 (2r) `
`=2 pi r^3`
So, the volume of the cylinder is `2 pi r^3` .
APPEARS IN
संबंधित प्रश्न
A model of a ship is made to a scale 1: 300
1) The length of the model of the ship is 2 m. Calculate the lengths of the ship.
2) The area of the deck ship is 180,000 m2. Calculate the area of the deck of the model.
3) The volume of the model in 6.5 m3. Calculate the volume of the ship.
A solid sphere of radius 15 cm is melted and recast into solid right circular cones of radius 2.5 cm and height 8 cm. Calculate the number of cones recast.
Find the total surface area of a hemisphere and a solid hemisphere each of radius 10 cm.
(Use 𝜋 = 3.14)
The surface area of a sphere is 5544 `cm^2`, find its diameter.
The surface area of a sphere is 2464 cm2, find its volume.
Eight metallic spheres; each of radius 2 mm, are melted and cast into a single sphere. Calculate the radius of the new sphere.
Total volume of three identical cones is the same as that of a bigger cone whose height is 9 cm and diameter 40 cm. Find the radius of the base of each smaller cone, if height of each is 108 cm.
Spherical marbles of diameter 1.4 cm are dropped into beaker containing some water and are fully submerged. The diameter of the beaker is 7 cm. Find how many marbles have been dropped in it if the water rises by 5.6 cm.
If a sphere of radius 2r has the same volume as that of a cone with circular base of radius r, then find the height of the cone.
Mark the correct alternative in each of the following:
In a sphere the number of faces is
A cone, a hemisphere and a cylinder stand on equal bases and have the same height. The ratio of their volumes is
Find the surface area and volume of sphere of the following radius. (π = 3.14)
4 cm
The radius of a sphere is 9 cm. It is melted and drawn into a wire of diameter 2 mm. Find the length of the wire in metre.
A sphere has the same curved surface area as the curved surface area of a cone of height 36 cm and base radius 15 cm . Find the radius of the sphere .
A solid metallic cylinder has a radius of 2 cm and is 45 cm tall. Find the number of metallic spheres of diameter 6 cm that can be made by recasting this cylinder .
The volume of a sphere is 905 1/7 cm3, find its diameter.
The radius of two spheres are in the ratio of 1 : 3. Find the ratio between their volume.
The cylinder of radius 12 cm have filled the 20 cm with water. One piece of iron drop in the stands of water goes up 6.75 cm. Find the radius of sphere piece.
A solid sphere is cut into two identical hemispheres.
Statement 1: The total volume of two hemispheres is equal to the volume of the original sphere.
Statement 2: The total surface area of two hemispheres together is equal to the surface area of the original sphere.
Which of the following is valid?
