Advertisements
Advertisements
Question
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.
Solution
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
RELATED QUESTIONS
A container shaped like a right circular cylinder having diameter 12 cm and height 15 cm is full of ice cream. The ice cream is to be filled into cones of height 12 cm and diameter 6 cm, having a hemispherical shape on the top. Find the number of such cones which can be filled with ice cream.
A well of diameter 3 m is dug 14 m deep. The soil taken out of it is spread evenly all around it to a width of 5 m to form an embankment. Find the height of the embankment ?
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 hemispherical bowl of internal radius 9 cm is full of liquid. The liquid is to be filled into cylindrical shaped small bottles each of diameter 3 cm and height 4 cm. How many bottles are necessary to empty the bowl?
A right circular cylinder of radius r and height h (h = 2r) just encloses a sphere of diameter
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
During conversion of a solid from one shape to another, the volume of the new shape will ______.
Water flows at the rate of 10m/minute through a cylindrical pipe 5 mm in diameter. How long would it take to fill a conical vessel whose diameter at the base is 40 cm and depth 24 cm?
A cylindrical bucket of height 32 cm and base radius 18 cm is filled with sand. This bucket is emptied on the ground and a conical heap of sand is formed. If the height of the conical heap is 24 cm, find the radius and slant height of the heap.
A solid piece of metal in the form of a cuboid of dimensions 11 cm × 7 cm × 7 cm is melted to form 'n' number of solid spheres of radii `7/2` cm each. Find the value of n.
