Advertisements
Advertisements
Question
A cone, a hemisphere and a cylinder stand on equal bases and have the same height. The ratio of their volumes is
Options
1 : 2 : 3
2 : 1 : 3
2 : 3 : 1
3 : 2 : 1
Advertisements
Solution
In the given problem, we are given a cone, a hemisphere and a cylinder which stand on equal bases and have equal heights. We need to find the ratio of their volumes.
So,
Let the radius of the cone, cylinder and hemisphere be x cm.
Now, the height of the hemisphere is equal to the radius of the hemisphere. So, the height of the cone and the cylinder will also be equal to the radius.
Therefore, the height of the cone, hemisphere and cylinder = x cm
Now, the next step is to find the volumes of each of these.
Volume of a cone (V1) = `(1/3)pi r^2 h`
`=(1/3)pi (x)^2 (x) `
`=(1/3) pi x^3`
Volume of a hemisphere (V2) = `(2/3) pi r^3`
`=(2/3) pi (x)^3`
`=(2/3) pi x^3`
Volume of a cylinder (V3) = `pi r^2 h`
`=pi(x)^2(x)`
`=pi x^3`
So, now the ratio of their volumes = (V1) : (V2) : (V3)
`=(1/3) pix^3 : (2/3) pi x^3 : pi x^3`
`=(1/3) pi x^3 : (2/3) pi x^3 : (3/3) pi x^3`
= 1: 2 : 3
Therefore, the ratio of the volumes of the given cone, hemisphere and the cylinder is 1: 2:3 .
APPEARS IN
RELATED QUESTIONS
Find the surface area of a sphere of radius 10.5 cm.
`["Assume "pi=22/7]`
Find the surface area of a sphere of radius 5.6 cm.
`["Assume "pi=22/7]`
The diameter of the moon is approximately one fourth of the diameter of the earth. Find the
ratio of their 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
The total area of a solid metallic sphere is 1256 cm2. It is melted and recast into solid right circular cones of radius 2.5 cm and height 8 cm. Calculate :
- the radius of the solid sphere.
- the number of cones recast. [Take π = 3.14]
A hemi-spherical bowl has negligible thickness and the length of its circumference is 198 cm. Find the capacity of the bowl.
Determine the ratio of the volume of a cube to that of a sphere which will exactly fit inside the cube.
If a sphere is inscribed in a cube, find the ratio of the volume of cube to the volume of the sphere.
Mark the correct alternative in each of the following:
In a sphere the number of faces is
The total surface area of a hemisphere of radius r is
If a sphere is inscribed in a cube, then the ratio of the volume of the sphere to the volume of the cube is
Find the radius of a sphere whose surface area is equal to the area of the circle of diameter 2.8 cm
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 .
The total area of a solid metallic sphere is 1256 cm2. It is melted and recast into solid right circular cones of radius 2.5 cm and height 8 cm. Calculate: the number of cones recasted [π = 3.14]
A conical tent is to accommodate 77 persons. Each person must have 16 m3 of air to breathe. Given the radius of the tent as 7 m, find the height of the tent and also its curved surface area.
Find the volume and surface area of a sphere of diameter 21 cm.
There is surface area and volume of a sphere equal, find the radius of sphere.
There is a ratio 1: 4 between the surface area of two spheres, find the ratio between their radius.
A spherical cannon ball, 28 cm in diameter is melted and recast into a right circular conical mould, the base of which is 35 cm in diameter. Find the height of the cone, correct to one place of decimal.
