Question

pragya donates toys to children of an orphanage.Each toy is in the shape of a cone mounted on a hemisphere mounted on a hemisphere of common base radius 7 cm total height of the toy is 31 Cm find the total surface area of the toy

Answer 1

According to questions,

radius of cone
r = 7 Cm
height of cone
h = 31 Cm

Also
radius of hemisphere
R = 7 Cm

Total surface area of Toy = surface area od cone + surface area of hemisphere
                                        = pi r( r + root (h^2 + r^2) ]  +   2 pi r^2
                                        = 22/7 * 7  [ 38.78 ]  + 2 * 22/7 * 49
                                         = 1161.16 Cm^2

Answer 2

Solution :-

Common base radius of the toy = 7 cm

Total height of the toy = 31 cm

Height of the conical part = total height - height of the hemispherical part 

31 - 7 = 24 cm

We know that,

Slant height 'l' = h² + r²

⇒ l² = 24² + 7²

⇒ l² = 576 + 49

⇒ l² = 625

⇒ l = √625

⇒ l = 25 cm

Surface area of the cone = πrl

⇒ 22/7*7*25

= 550 cm²

Surface area of hemispherical part = 2πr²

⇒ 2*22/7*7*7

= 308 cm²

Total surface area of the toy = Surface area of the conical part + Surface area of the hemispherical part 

⇒ 550 + 308

= 858 cm²

Answer.