Advertisements
Advertisements
प्रश्न
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.
उत्तर
Let the number of small cones be 'n'
Volume of sphere
= `4/3pi(8^3 - 6^3)`
= `4/3 xx pi xx 2 xx 148`
Volume of small cones
= `1/3pir^2h`
= `1/3 xx pi xx 2^2 xx 4`
Volume of sphere = n × Volume of small cones
`=> 4/3 xx pi xx 2 xx 148 = n xx 1/3 xx pi xx 2^2 xx 8`
`=> n = (4 xx 2 xx 148 xx 3)/(4 xx 8 xx 3)`
`=>` n = 37
The number of cones = 37 cm.
APPEARS IN
संबंधित प्रश्न
Find the surface area of a sphere of radius 14 cm.
`["Assume "pi=22/7]`
Find the surface area of a sphere of radius 5.6 cm .
Find the surface area of a sphere of diameter 3.5 cm .
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.
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 Rs. 4 per 100 `cm^2`
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 wooden toy is in the form of a cone surmounted on a hemisphere. The diameter of the base
of the cone is 16 cm and its height is 15 cm. Find the cost of painting the toy at Rs. 7 per 100
`cm^2`.
Eight metallic spheres; each of radius 2 mm, are melted and cast into a single sphere. Calculate the radius of the new sphere.
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?
Mark the correct alternative in each of the following:
In a sphere the number of faces is
If the radius of a solid hemisphere is 5 cm, then find its curved surface area and total surface area. ( π = 3.14 )
If the surface area of a sphere is 2826 cm2 then find its volume. ( π= 3.14)
Find the radius of the sphere whose surface area is equal to its volume .
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 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.
There is a ratio 1: 4 between the surface area of two spheres, find the ratio between their radius.
The radius of two spheres are in the ratio of 1 : 3. Find the ratio between their volume.
A vessel is in he form of an inverted cone. Its height is 11 cm., and the radius of its top which is open is 2.5 cm. It is filled with water up to the rim. When lead shots, each of which is a sphere of radius 0.25 cm., are dropped 2 into the vessel, `2/5`th of the water flows out. Find the number of lead shots dropped into the vessel.
The radius of a sphere is 10 cm. If we increase the radius 5% then how many % will increase in volume?
