Advertisements
Advertisements
Question
A sphere and a cube are of the same height. The ratio of their volumes is
Options
3 : 4
21 : 11
4 : 3
11 : 21
Advertisements
Solution
In the given problem, we have a sphere and a cube of equal heights. So, let the diameter of the sphere and side of the cube be x units.
So, volume of the sphere (V1) = `4/3 pi (d/2)^3`
`=4/3 pi (x/2)^3`
`=4/3 pi (x^3 /8)`
`= (pi x^3)/6`
Volume of the cube (V2) = S3
= x3
So, to find the ratio of the volumes,
`V_1/V-2 = (pi x^3/6)/x^3`
` = pi /6`
` = ((22/7))/6`
`=11/21 `
Therefore, the ratio of the volumes of sphere and cube of equal heights is 11 : 21.
APPEARS IN
RELATED QUESTIONS
Find the surface area of a sphere of diameter 21 cm.
`["Assume "pi=22/7]`
A hemispherical bowl made of brass has inner diameter 10.5 cm. Find the cost of tin-plating it on the inside at the rate of ₹ 16 per 100 cm2.
`["Assume "pi=22/7]`
Two solid spheres of radii 2 cm and 4 cm are melted and recast into a cone of height 8 cm. Find the radius of the cone so formed.
A hollow sphere of internal and external radii 6 cm and 8 cm respectively is melted and recast into small cones of base radius 2 cm and height 8 cm. Find the number of cones.
Assuming the earth to be a sphere of radius 6370 km, how many square kilo metres is area
of the land, if three-fourth of the earth’s surface is covered by water?
A cylinder of same height and radius is placed on the top of a hemisphere. Find the curved
surface area of the shape if the length of the shape be 7 cm.
The diameter of a sphere is 6 cm. It is melted and drawn into a wire of diameter 0.2 cm. Find the length of the wire.
Find the total surface area of a hemisphere of radius 10 cm.
Find the radius of a sphere whose surface area is 154 cm2.
How many spherical bullets can be made out of a solid cube of lead whose edge measures 44 cm, each bullet being 4 cm in diameter?
If a solid sphere of radius r is melted and cast into the shape of a solid cone of height r, then the radius of the base of the cone is
A cone and a hemisphere have equal bases and equal volumes the ratio of their heights is
Find the radius of the sphere whose surface area is equal to its volume .
Find the volume of the hollow sphere whose inner diameter is 8 cm and the thickness of the material of which it is made is 1 cm .
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]
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 number of cones recast. `("Take" pi =22/7)`
The given figure shows the cross-section of a cone, a cylinder and a hemisphere all with the same diameter 10 cm and the other dimensions are as shown.
Calculate :
- the total surface area.
- the total volume of the solid and
- the density of the material if its total weight is 1.7 kg.
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.
The radius of a sphere increases by 25%. Find the percentage increase in its surface area
The radius of a hemispherical balloon increases from 6 cm to 12 cm as air is being pumped into it. The ratios of the surface areas of the balloon in the two cases is ______.
