Advertisements
Advertisements
Question
A solid metallic sphere of diameter 21 cm is melted and recast into a number of smaller cones, each of diameter 3.5 cm and height 3 cm. Find the number of cones so formed.
Solution
Diameter of sphere = 21 cm
Radius of sphere =`21/2` cm
Volume of sphere `= 4/3 pir^3 = (4xx21xx21xx21xx21pi)/(3xx2xx2xx2)= (21xx21xx21pi)/(3xx2) "cm"^3`
Diameter of the cone = 3.5 cm
Radius of the cone `= 3.5/2 = 7/4 "cm"`
Height = 3 cm
Volume of each cone` = 1/3pir^2h xx 1/3pixx3xx(7/4)^2 = (7/4)^2 pi "cm"^3 `
`"Total number of cones"= "Volume of sphere"/"Volume of a cone" = ((21xx21xx21pi)/(3xx2))/((7/4)^2pi) = (21xx21xx21xxpixx4xx4)/3xx2xxpixx)`
APPEARS IN
RELATED QUESTIONS
A toy is in the form of a cone surmounted on a hemisphere. The diameter of the base and the height of cone are 6cm and 4cm. determine surface area of toy?
If the radii of circular ends of a bucket 24cm high are 5cm and 15cm. find surface area of
bucket?
A cylindrical tub, whose diameter is 12 cm and height 15 cm is full of ice-cream. The whole ice-cream is to be divided into 10 children in equal ice-cream cones, with conical base surmounted by hemispherical top. If the height of conical portion is twice the diameter of base, find the diameter of conical part of ice-cream cone ?
In Figure 4, from a rectangular region ABCD with AB = 20 cm, a right triangle AED with AE = 9 cm and DE = 12 cm, is cut off. On the other end, taking BC as diameter, a semicircle is added on outside the region. Find the area of the shaded region.\[[Use\pi = 3 . 14]\]
How many spherical lead shots each of diameter 4.2 cm can be obtained from a solid rectangular lead piece with dimension 6cm \[\times\] 42cm \[\times\] 21 cm.
From a solid cube of side 7 cm , a conical cavity of height 7 cm and radius 3 cm is hollowed out . Find the volume of the remaining solid.
A copper wire of diameter 6 mm is evenly wrapped on a cylinder of length 18 cm and diameter 49 cm to cover its whole surface. Find the length and the volume of the wire. If the density of the copper be 8.8 g per cm3, then find the weight of the wire.
If the volumes of a cube is 1728 cm³, the length of its edge is equal to ______.
The radius of spherical balloon increases from 8 cm to 12 cm. The ratio of the surface areas of balloon in two cases is ______.
Two identical solid hemispheres of equal base radius r cm are stuck together along their bases. The total surface area of the combination is 6πr2.
