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Question
A vessel is in the form of a hollow hemisphere mounted by a hollow cylinder. The diameter of the hemisphere is 14 cm and the total height of the vessel is 13 cm. Find the inner surface area of the vessel. [Use `pi = 22/7`]
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Solution
It can be observed that the radius (r) of the cylindrical part and the hemispherical part is the same (i.e., 7 cm).
Height of hemispherical part = Radius = 7 cm
Height of cylindrical part (h) = 13 − 7 = 6 cm
Inner surface area of the vessel = CSA of cylindrical part + CSA of hemispherical part
= 2πrh + 2πr2
Inner surface are of vessel = `2 xx 22/7 xx 7 xx 6+2 xx 22/7 xx 7 xx 7`
= 44 (6 + 7)
= `44xx13`
= 572 cm2
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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:
- The internal radius of hemispherical bowl (filled completely with water) in I is 9 cm and the radius and height of the cylindrical jar in II are 1.5 cm and 4 cm respectively. If the hemispherical bowl is to be emptied in cylindrical jars, then how many cylindrical jars are required?
- 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?
