Advertisements
Advertisements
प्रश्न
The radius of a metal sphere is 3 cm. The sphere is melted and made into a long wire of uniform circular cross-section, whose length is 36 cm. To calculate the radius of wire, complete the following activity.
Radius of the sphere = `square`
Length of the wire = `square`
Let the radius of the wire by r cm.
Now, Volume of the wire = Volume of the `square`
`square` = `square`
r2 × `square` = `square` × `square`
r2 × `square` = `square`
r = `square`
Hence, the radius of the wire is `square` cm.
उत्तर
Radius of the sphere = 3 cm
Length of the wire = 36 cm
Let the radius of the wire by r cm.
Now, Volume of the wire = Volume of the sphere
πr2h = `bb(4/3)` πR3
r2 × 36 = `bb(4/3)` × 33
r2 × 36 = 36
r = 1
Hence, the radius of the wire is 1 cm.
APPEARS IN
संबंधित प्रश्न
In a rain-water harvesting system, the rain-water from a roof of 22 m × 20 m drains into a cylindrical tank having diameter of base 2 m and height 3·5 m. If the tank is full, find the rainfall in cm. Write your views on water conservation.
Two spheres of same metal weigh 1 kg and 7 kg. The radius of the smaller sphere is 3 cm. The two spheres are melted to form a single big sphere. Find the diameter of the new sphere ?
Find the surface area of a sphere of radius 7 cm.
Water is flowing at the rate of 15 km/hour through a pipe of diameter 14 cm into a cuboidal pond which is 50 m long and 44 m wide. In what time will the level of water in the pond rise by 21 cm?
A canal is 300 cm wide and 120 cm deep. The water in the canal is flowing with a speed of 20 km/hr. How much area will it irrigate in 20 minutes if 8 cm of standing water is desired ?
A building is in the form of a cylinder surmounted by a hemi-spherical vaulted dome and contains \[41\frac{19}{21} m^3\] of air. If the internal diameter of dome is equal to its total height above the floor , find the height of the building ?
A tent of height 8.25 m is in the form of a right circular cylinder with diameter of base 30 m and height 5.5 m, surmounted by a right circular cone of the same base. Find the cost of the canvas of the tent at the rate of Rs 45 per m2.
A cylinder, a cone and a hemisphere are of equal base and have the same height. What is the ratio of their volumes?
Water flows at the rate of 10 metre per minute from a cylindrical pipe 5 mm in diameter. How long will it take to fill up a conical vessel whose diameter at the base is 40 cm and depth 24 cm?
66 cubic cm of silver is drawn into a wire 1 mm in diameter. Calculate the length of the wire in metres.
A sphere of diameter 18 cm is dropped into a cylindrical vessel of diameter 36 cm, partly filled with water. If the sphere is completely submerged, then the water level rises by ______.
The volume of a cube is 2744 cm2. Its surface area is
The sum of length, breadth and height of a cuboid is 19 cm and its diagonal is `5sqrt(5)` cm. Its surface area is
The surface area of a sphere is 154 cm2. The volume of the sphere is
If the radii of the ends of a bucket are 5 cm and 15 cm and it is 24 cm high, then its surface area is
A toy is in the form of a cone mounted on a hemisphere of common base radius 7 cm. The total height of the toy is 31 cm. Find the total surface area of the toy.
In Figure 3, a decorative block is shown which is made of two solids, a cube, and a hemisphere. The base of the block is a cube with an edge 6 cm and the hemisphere fixed on the top has a diameter of 4⋅2 cm. Find
(a) the total surface area of the block.
(b) the volume of the block formed. `("Take" pi = 22/7)`
The slant height of a bucket is 26 cm. The diameter of upper and lower circular ends are 36 cm and 16 cm. then height of bucket is ______.
The surface area of a sphere is 616 cm2. Its radius is ______.
______ surface area of room = area of 4 walls.
