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प्रश्न
A hemispherical bowl of internal diameter 30 cm contains some liquid. This liquid is to be poured into cylindrical bottles of diameter 5 cm and height 6 cm each. Find the number of bottles required.
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उत्तर
Inner diameter of the bowl = 30 cm
Inner radius of the bowl `=(30 "cm")/2= 15 "cm"`
Volume of liquid `= 2/3pir^3 =2/3xxpixx15^3 "cm"^3`
Radius of each bottle = 2.5 cm
Height = 6 cm
Volume of each bottl `=pir^2h = pixx5/2xx5/2xx6=(75pi)/2 "cm"^3`
total number of bottles required `=[(2/3pixx15xx15xx15xx6)/((75pi)/2)]= (2pixx15xx15xx15xx2)/(3xx75pi) = 15xx14=60`
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Students found the shapes of the objects very interesting and they could easily relate them with mathematical shapes viz sphere, hemisphere, cylinder etc. |
Maths teacher who was accompanying the students asked the following questions:
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- If in the cylindrical jar full of water, a conical funnel of the same height and same diameter is immersed, then how much water will flow out of the jar?
The boilers are used in thermal power plants to store water and then used to produce steam. One such boiler consists of a cylindrical part in middle and two hemispherical parts at its both ends.
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Find the total surface area and the volume of the boiler. Also, find the ratio of the volume of cylindrical part to the volume of one hemispherical part.
