Advertisements
Advertisements
प्रश्न
A solid metallic sphere of diameter 8 cm is melted and drawn into a cylindrical wire of uniform width. If the length of the wire is 12 m, then find its width.
उत्तर
We have,
Radius of the metallic sphere, R`= 8/2 = 4 "cm"` and
Height of the cylindrical wire, h = 12 m = 1200 cm
Let The radius cylindrical wire, h = 12 m = 1200 cm
Let the radius of the base be r.
Now,
Volume of the cylindrical wire = Volume of the metallic sphere
`=> pi"r"^2"h" = 4/3 pi"R"^3`
`=> "r"^2 = (4"R"^3)/(3"h")`
`=> "r"^2 = (4xx4xx4xx4)/(3xx1200)`
`=> "r"^2 = 16/225`
`=> "r" =sqrt(16/25)`
`=> "r" = 4/15 "cm"`
∴ The width of the wire = 2r
`=2xx4/15`
`=8/15 "cm"`
So, the width of the wire is `8/15` cm.
APPEARS IN
संबंधित प्रश्न
The dimensions of a solid iron cuboid are 4·4 m × 2·6 m × 1·0 m. It is melted and recast into a hollow cylindrical pipe of 30 cm inner radius and thickness 5 cm. Find the length of the pipe
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 ?
In the middle of a rectangular field measuring 30 m × 20 m, a well of 7 m diameter and 10 m depth is dug. The earth so removed is evenly spread over the remaining part of the field. Find the height through which the level of the field is raised.
The radii of the ends of a bucket 30 cm high are 21 cm and 7 cm. Find its capacity in litres and the amount of sheet required to make this bucket.
Two right circular cylinders of equal volumes have their heights in the ratio 1 : 2. What is the ratio of their radii ?
A cylindrical vessel of radius 4 cm contains water. A solid sphere of radius 3 cm is lowered into the water until it is completely immersed. The water level in the vessel will rise by
Choose the correct answer of the following question:
The surface areas of two spheres are in the ratio 16 : 9. The ratio of their volumes is
Choose the correct answer of the following question:
The radii of the circular ends of a bucket of height 40 cm are 24 cm and 15 cm. The slant height (in cm) of the bucket is
Assertion (A)
The curved surface area of a cone of base radius 3 cm and height 4 cm is 15π cm2.\
Reason (R)
Volume of a cone = πr2h
- Both Assertion (A) and Reason (R) are true and Reason (R) is a correct explanation of Assertion (A).
- Both Assertion (A) and Reason (R) are true but Reason (R) is not a correct explanation of Assertion (A).
- Assertion (A) is true and Reason (R) is false.
- Assertion (A) is false and Reason (R) is true.
The length, breadth and height of a cuboidal reservoir is 7 m, 6 m and 15 m respectively. 8400 L of water is pumped out from the reservoir. Find the fall in the water level in the reservoir.
