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Question
A toy is in the form of a cone of radius 3.5 cm mounted on a hemisphere of same radius. The total height of the toy is 15.5 cm. Find the total
surface area of the toy.
Solution
We have,
Radius of the hemisphere = Radius of the cone = r = 3.5 cm and
Height of the cone = 15.5 - 3.5 = 12 cm
Also,
The slant height of the cone,` "l" = sqrt("h"^2 +"r"^2)`'
`= sqrt(12^2+3.5^2)`
`=sqrt(144+12.25)`
`=sqrt(156.25)`
=12.5 cm
Now,
Total surface area of the toy = CSA of cone + CSA of hemisphere
`=pi"rl" + 2pi"r"^2`
`=pir("l"+2"r")`
`=22/7xx3.5xx(12.5+2xx3.5)`
`=11xx(12.5 + 7)`
`=11xx19.5`
=214.5 cm2
So, the total surface area of the toy is 214.5 cm2.
Disclaimer: The answer given in the textbook is incorrect. The same has been corrected above.
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