Advertisements
Advertisements
प्रश्न
What length of a solid cylinder 2cm in diameter must be taken to recast into a hollow
cylinder of length 16cm, external diameter 20cm and thickness 2.5mm?
उत्तर
Given that diameter of solid cylinder = 2cm
Given that solid cylinder is recast to hollow cylinder Length of hollow cylinder =16cm
External diameter = 20cm
Thickness = 2.5mm= 0.25cm
Volume of solid cylinder=`pir^2h`
Radius of cylinder =1cm
So volume of solid cylinder=`pi(1)^ 2h` ...........(i)
Let length of solid cylinder be h
Volume of hollow cylinder=`pih(R^2-r^2)`
Thickness =R - r
0.25 = 10 - r
⇒ Internal radius= 9.75cm
So volume of hollow cylinder = π x 16(100 - 95.0625) .........(2)
Volume of solid cylinder is equal to volume of hollow cylinder.
(1)=(2)
Equating equations (1) and (2)
`pi(1)^2h=pixx16(100-95.06)`
`22/7(1)^2xxh=22/7xx16(4.94)`
h=79.04cm
∴Length of solid cylinder =79cm
APPEARS IN
संबंधित प्रश्न
A solid consisting of a right circular cone of height 120 cm and radius 60 cm standing on a hemisphere of radius 60 cm is placed upright in a right circular cylinder full of water such that it touches the bottom. Find the volume of water left in the cylinder, if the radius of the cylinder is 60 cm and its height is 180 cm. Use [π = `22/7`]
A hemispherical tank, of diameter 3 m, is full of water. It is being emptied by a pipe at the rate of \[3\frac{4}{7}\] litre per second. How much time will it take to make the tank half empty?\[\left[ Use \pi = \frac{22}{7} \right]\]
The radii of two cylinders are in the ratio of 2 : 3 and their heights are in the ratio of 5 : 3. Find the ratio of their volumes.
A metallic cone of radius 12 cm and height 24 cm is melted and made into spheres of radius 2 cm each. How many spheres are formed?
Choose the correct answer of the following question:
If the radius of the base of a right circular cylinder is halved, keeping the height the same, then the ratio of the volume of the cylinder thus obtained to the volume of original cylinder is
A solid metallic sphere of diameter 21 cm is melted and recast into small cones of diameter 3.5 cm and height 3 cm each. Find the number of cones so formed.
In the equilateral Δ ABC of side 14 cm, side BC is the diameter of a semicircle as shown in the figure below. Find the area of the shaded region. (Take π = 22/7 and √3 = 1.732)
Three metallic solid cubes whose edges are 3 cm, 4 cm and 5 cm are melted and formed into a single cube. Find the edge of the cube so formed.
The rain water from a roof of dimensions 22 m × 20 m drains into a cylindrical vessel having diameter of base 2 m and height 3.5 m. If the rain water collected from the roof just fill the cylindrical vessel, then find the rainfall in cm.
A solid is in the shape of a cone standing on a hemisphere with both their diameters being equal to 1 cm and the height of the cone is equal to its radius. Find the volume of the solid. [Use π = 3.14]
