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
A right circular cylinder just encloses a sphere of radius r (see figure). Find
- surface area of the sphere,
- curved surface area of the cylinder,
- ratio of the areas obtained in (i) and (ii).
On a map drawn to a scale of 1: 50,000, a rectangular plot of land ABCD has the following dimensions. AB = 6 cm; BC = 8 cm and all angles are right angles. Find:
1) the actual length of the diagonal distance AC of the plot in km.
2) the actual area of the plot in sq. km.
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 the moon is approximately one fourth of the diameter of the earth. Find the
ratio of their surface areas.
A hemi-spherical dome of a building needs to be painted. If the circumference of the base of
the dome is 17.6 cm, find the cost of painting it, given the cost of painting is Rs. 5 per l00
`cm^2`
The surface area of a sphere is 2464 cm2, find its volume.
How many balls each of radius 1 cm can be made by melting a bigger ball whose diameter is 8 cm?
A largest sphere is to be carved out of a right circular cylinder of radius 7 cm and height 14 cm. Find the volume of the sphere.
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.
A sphere and a cube are of the same height. The ratio of their volumes is
Find the surface area and volume of sphere of the following radius. (π = 3.14 )
9 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.
How many lead balls of radii 1 cm each can be made from a sphere of 8 cm radius?
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, 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.
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 two spheres are in the ratio of 1 : 3. Find the ratio between their volume.
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?
The internal and external diameters of a hollow hemispherical vessel are 20 cm and 28 cm respectively. Find the cost to paint the vessel all over at ₹ 0.14 per cm2
