Advertisements
Advertisements
Question
The ratio between the volume of a sphere and volume of a circumscribing right circular cylinder is
Options
2 : 1
1 : 1
2 : 3
1 : 2
Advertisements
Solution
In the given problem, we need to find the ratio between the volume of a sphere and volume of a circumscribing right circular cylinder. This means that the diameter of the sphere and the cylinder are the same. Let us take the diameter as d.
Here,
Volume of a sphere (V1) = `(4/3) pi (d/2)^3`
`(4/3) pi (d^3/8)`
`= (pi d^3 ) /6`
As the cylinder is circumscribing the height of the cylinder will also be equal to the height of the sphere. So,
Volume of a cylinder (V2) = `pi (d/2)^2 h`
`= pi d^2/4(d)`
`=(pi d^3)/4`
Now, the ratio of the volume of sphere to the volume of the cylinder = `V_1/V_2`
`V_1/V_2=(((pid^3)/6))/(((pi d^3)/4))`
`=4/6`
`=2/3`
So, the ratio of the volume of sphere to the volume of the cylinder is 2: 3 .
APPEARS IN
RELATED QUESTIONS
Find the surface area of a sphere of radius 5.6 cm.
`["Assume "pi=22/7]`
The radius of a spherical balloon increases from 7 cm to 14 cm as air is being pumped into it. Find the ratio of surface areas of the balloon in the two cases.
Find the radius of a sphere whose surface area is 154 cm2.
`["Assume "pi=22/7]`
The surface area of a solid metallic sphere is 2464 cm2. It is melted and recast into solid right circular cones of radius 3.5 cm and height 7 cm. Calculate:
- the radius of the sphere.
- the number of cones recast. (Take π = `22/7`)
A solid cone of radius 5 cm and height 8 cm is melted and made into small spheres of radius 0.5 cm. Find the number of spheres formed.
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.
The volume of one sphere is 27 times that of another sphere. Calculate the ratio of their :
- radii,
- surface areas.
Metallic spheres of radii 6 cm, 8 cm and 10 cm respectively are melted and recasted into a single solid sphere. Taking π = 3.1, find the surface area of the solid sphere formed.
The surface area of a solid sphere is increased by 12% without changing its shape. Find the percentage increase in its:
- radius
- volume
A hollow sphere of internal and external diameter 4 cm and 8 cm respectively is melted into a cone of base diameter 8 cm. Find the height of the cone.
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.
The hollow sphere, in which the circus motor cyclist performs his stunts, has a diameter of 7 m. Find the area available to the motorcyclist for riding.
The surface area of a sphere of radius 5 cm is five times the area of the curved surface of a cone of radius 4 cm. Find the height of the cone.
Mark the correct alternative in each of the following:
In a sphere the number of faces is
How many lead balls of radii 1 cm each can be made from a sphere of 8 cm radius?
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 .
A solid, consisting of a right circular cone standing on a hemisphere, is placed upright, in a right circular cylinder, full of water and touches the bottom. Find the volume of water left in the cylinder, having given that the radius of the cylinder is 3 cm and its height is 6 cm; the radius of the hemisphere is 2 cm and the height of the cone is 4 cm. Give your answer to the nearest cubic centimetre.
Find the volume and surface area of a sphere of diameter 21 cm.
A manufacturing company prepares spherical ball bearings, each of radius 7 mm and mass 4 gm. These ball bearings are packed into boxes. Each box can have a maximum of 2156 cm3 of ball bearings. Find the:
- maximum number of ball bearings that each box can have.
- mass of each box of ball bearings in kg.
(Use π = `22/7`)
