Advertisements
Advertisements
प्रश्न
A cylindrical container is filled with ice-cream, whose diameter is 12 cm and height is 15 cm. the whole ice-cream is distributed to 10 children in equal cones having hemispherical tops. If the height of the conical portion is twice the diameter of its base, find the diameter of the ice-cream.
उत्तर
Volume of cylindrical container
`=pir^2h`
`=pi xx (6)^2 xx 15`
Amount of ice-cream distributed to 10 children
`=(pi xx (6)^2 xx 15)/10`
Therefore,
Height of conical portion = 2 × diameter of its bars
Let the diameter of bare = r
Height = 2r
Therefore,
Volume of the cones
`= 1/3 pi (r/2)^2 h + 2/3 pir^3`
` = 1/3 pi (r/2)^2 (h + 2r)`
`=1/3pi xx (r/2)^2 (2r + 2 xx r/2)`
`=1/3 pi xx (r/2)^2 xx 3`
`r = (pir^3)/4`
Therefore,
Volume of the cones = amount distributed
`(pir^3)/4 = (pi(6)^2 xx 15)/10`
`r^3 = (4 xx 6 xx 6 xx 15)/10 = 4xx 6 xx 9`
`r = 3sqrt(6 xx 6 xx 6) = 6cm`
APPEARS IN
संबंधित प्रश्न
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 ?
A solid sphere of radius 10.5 cm is melted and recast into smaller solid cones, each of radius 3.5 cm and height 3 cm.Find the number of cones so formed.
Water flows at the rate of 15 km/hr 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.
Two cubes have their volumes in the ratio 1 : 27. What is the ratio of their surface areas?
The inner diameter of a glass is 7 cm and it has a raised portion in the bottom in the shape of a hemisphere, as shown in the figure. If the height of the glass is 16 cm, find the apparent capacity and the actual capacity of the glass.
A hemispherical tank, full of water, is emptied by a pipe at the rate of `25/7` litres per second. How much time will it take to empty half the tank if the diameter of the base of the tank is 3 m?
If the area of the base of a right circular cone is 3850 cm2 and its height is 84 cm, then find the slant height of the cone.
The slant height of a bucket is 45 cm and the radii of its top and bottom are 28 cm and 7 cm, respectively. The curved surface area of the bucket is
The ratio of the total surface area to the lateral surface area of a cylinder with base radius 80 cm and height 20 cm is
A rectangular examination hall having seats for 500 candidates has to be built so as to allow 4 cubic metres of air and 0.5 square metres of floor area per candidate. If the length of hall be 25 m, find the height and breadth of the hall.
