question_answer

A toy is in the form of a cone mounted on a hemisphere such that the diameter of the base of the cone is equal to that of the hemisphere. If the diameter of the base of the cone is 6 cm and its height is 4 cm, what is the surface area of the toy in \[c{{m}^{2}}\]?    (Take\[\pi =3.14\])

A) \[93.62\]                      

B) \[103.62\]

C) \[113.62\]                    

D) \[115.50\]

Correct Answer: B

Solution :

Surface area of Toy = curved surface area of cone + curved surface area of hemisphere CSA of cone \[=\pi \,rl\] \[=3.14\times 3\times \sqrt{{{4}^{2}}+{{3}^{2}}}\,\,\,(l=\sqrt{{{r}^{2}}+{{h}^{2}}})\] \[=3.14\times 3\times 5=15\times 3.14\] CSA of hemisphere \[=2\,\,\pi \,\,{{r}^{2}}\] \[=2\times 3.14\times {{(3)}^{2}}=3.14\times 18\] surface area of Toy \[=3.14\times 15+3.14\times 18\] \[=3.14\times 33=\]