Advertisements
Advertisements
प्रश्न
The internal and external diameters of a hollow hemispherical shell are 6 cm and 10 cm, respectively. It is melted and recast into a solid cone of base diameter 14 cm. Find the height of the cone so formed.
उत्तर
Internal diameter of the hemispherical shell = 6 cm
Therefore, internal radius of the hemispherical shell = 3 cm
External diameter of the hemispherical shell = 10 cm
External radius of the hemispherical shell = 5 cm
Volume of hemispherical shell `= 2/3 pi (5^3 -3^3) = 196/3xx22/7=616/3 "cm"^3`
Radius of cone = 7 cm
Let the height of the cone be h cm.
Volume of cone =` 1/3pir^2h = 1/3xx22/7xx7xx7h= (154h)/3 "cm"^3`
The volume of the hemispherical shell must be euqal to the volume of the cone therefore
`(154h)/3 = 616/3`
`rArr h = 616/154 =4 "cm"`
APPEARS IN
संबंधित प्रश्न
A 20 m deep well with diameter 7 m is dug and the earth from digging is evenly spread out to form a platform 22 m by 14 m. Find the height of the platform. [Use Π = 22/7]
How many silver coins, 1.75 cm in diameter and of thickness 2 mm, must be melted to form a cuboid of dimensions 5.5 cm × 10 cm × 3.5 cm? [Use π=22/7]
How many spherical lead shots of diameter 4 cm can be made out of a solid cube of lead whose edge measures 44 cm .
A solid cylinder of diameter 12 cm and height 15 cm is melted and recast into toys with the shape of a right circular cone mounted on a hemisphere of radius 3 cm.If the height of the toy is 12 cm, find the number of toys so formed.
The radii of the ends of a bucket 16 cm height are 20 cm and 8 cm. The curved surface area of the bucket is
If two solid-hemisphere s of same base radius r are joined together along their bases , then curved surface area of this new solid is
A right circular cylinder of radius r cm and height h cm (h > 2r) just encloses a sphere of diameter ______.
A solid cylinder of radius r and height h is placed over other cylinder of same height and radius. The total surface area of the shape so formed is ______.
A solid metallic hemisphere of radius 8 cm is melted and recasted into a right circular cone of base radius 6 cm. Determine the height of the cone.
The volume of a right circular cone whose area of the base is 156 cm2 and the vertical height is 8 cm, is ______.
