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प्रश्न
Two cones with same base radius 8 cm and height 15 cm are joined together along their bases. Find the surface area of the shape so formed.
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उत्तर
According to the question,
We get the figure given below,
We know that,
Total surface area of shape formed = Curved area of first cone + Curved surface area of second cone
Since, both cones are identical,
We have,
Total surface area of shape formed = Curved area of first cone + Curved surface area of the second cone
= 2(Surface area of cone)
We also know that,
Surface area of cone = πrl, where r = radius and l = slant height
And the total surface area of shape so formed = 2πrl
Given in the question that,
Radius, r = 8 cm
Height, h = 15 cm
Therefore,
Area = Curved area of first cone + Curved surface area of the second cone
= 2(Surface area of the cone)
= 2 × πrl
= `2 xx π xx "r" xx sqrt("r"^2 + "h"^2)`
= `2 xx 22/7 xx 8 xx sqrt(8^2 + 15^2)`
= `50.28 xx sqrt(289)`
= 854.85 cm2
= 855 cm2 ...(Approx)
Hence, the surface area of shape so formed is 855cm2.
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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?
