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प्रश्न
A cylinder, a cone and a hemisphere are of equal base and have the same height. What is the ratio of their volumes?
उत्तर
Let the diameter of the base for all three be x cm and height be y cm.
For hemisphere radius `x /2 cm`
Height `y = x/2 cm`
(As height of the hemisphere is equal to the radius of hemisphere)
For cone
Radius `= x /2 cm`
Height `= x /2 cm`
(As height is same for all)
For cylinder
Radius `= x /2 cm`
Height `= x /2 cm`
The ratio of their volume is
= cylinder volume : conic volume : hemispherical volume
` = pi (x/2)^2 x /2 :1/3 pi (x/2)^2 (x/2) :2/3 pi (x/3)^3`
`=1 :1/3 :2/3`
`=3:1:2`
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संबंधित प्रश्न
Due to heavy floods in a state, thousands were rendered homeless. 50 schools collectively offered to the state government to provide place and the canvas for 1500 tents to be fixed by the governments and decided to share the whole expenditure equally. The lower part of each tent is cylindrical of base radius 2.8 cm and height 3.5 m, with conical upper part of same base radius but of height 2.1 m. If the canvas used to make the tents costs Rs. 120 per sq. m, find the amount shared by each school to set up the tents. What value is generated by the above problem? (use `pi =22/7`)
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Activity: Radius of the sphere, r = 18 cm
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∴ Number of cylinders can be made =`"Volume of the sphere"/square`
`= (4/3 pir^3)/square`
`= (4/3 xx 18 xx 18 xx 18)/square`
= `square`
