Advertisements
Advertisements
प्रश्न
A hollow metallic sphere with external diameter 8 cm and internal diameter 4 cm is melted and moulded into a cone of base radius 8 cm. The height of the cone is
विकल्प
12 cm
14 cm
15 cm
18 cm
3 . 5 cm
उत्तर
External diameter = 8 cm
Internal diameter = 4 cm
Let the external and internal radii of the hollow metallic sphere be R and r, respectively.
Then,
External radius `8/2 = 4 "cm"`
Internal Radius = `4/2 = 2 "cm"`
Then, volume of the hollow sphere:
`4/3pi[("R")^3 - ("r")^3]`
`= 4/3 pi [(4)^3 - (2)^3]`
Therefore,
Volume of the hollow sphere
`4/3pi[(4)^3 - (2)^3] = 1/3pixx(8)^2 xx "h"`
`=> 4 (64-8) = 64 × "h" `
`=> 224 = 64 × "h" `
`=> "h" = 224/64`
⇒ h = 3.5 cm
APPEARS IN
संबंधित प्रश्न
How many spherical bullets each of 5cm in diameter can be cast from a rectangular block of metal 11 dm x 1m x 5 dm?
A rectangular tank 15m long and 11m broad is required to receive entire liquid contents from a full cylindrical tank of internal diameter 21m and length 5m. Find least height of tank that will serve purpose .
An iron spherical ball has been melted and recast into smaller balls of equal size. If the radius of each of the smaller balls is 1/4 of the radius of the original ball, how many such balls are made? Compare the surface area, of all the smaller balls combined together with that of the original ball.
A cylindrical tub of radius 5 cm and length 9.8 cm is full of water. A solid in the form of a right circular cone mounted on a hemisphere is immersed in the tub. If the radius of the hemisphere is immersed in the tub. If the radius of the hemi-sphere is 3.5 cm and height of the cone outside the hemisphere is 5 cm, find the volume of the water left in the tub (Take π = 22/7)
A metallic right circular cone 20cm high and whose vertical angle is 90° is cut into two parts at the middle point of its axis by a plane parallel to base. If frustum so obtained bee
drawn into a wire of diameter
(1/16) cm find length of the wire?
12 spheres of the same size are made from melting a solid cylinder of 16 cm diameter and 2 cm height. The diameter of each sphere is
A solid is in the form of a right circular cone mounted on a hemisphere. The radius of the hemisphere is 2.1 cm and the height of the cone is 4 cm. The solid is placed in a cylindrical tub full of water in such a way that the whole solid is submerged in water. If the radius of the cylinder is 5 cm and its height is 9.8 cm, find the volume of the water left in the tub.
A mason constructs a wall of dimensions (270 cm × 300 cm × 350 cm) with bricks, each of size (22.5 cm × 11.25 cm × 8.75 cm) and it is assumed that `1/8` space is covered by the mortar. Number of bricks used to construct the wall is ______.
From a solid cube of side 7 cm, a conical cavity of height 7 cm and radius 3 cm is hollowed out. Find the volume of the remaining solid.
How many cubic centimetres of iron is required to construct an open box whose external dimensions are 36 cm, 25 cm and 16.5 cm provided the thickness of the iron is 1.5 cm. If one cubic cm of iron weighs 7.5 g, find the weight of the box.
