A Toy in the Form of 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 toy. | Bzziii

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A toy in the form of 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 toy.







Given,

Radius of cone = 3.5 cm, height of cone = 15.5 – 3.5 = 12 cm

Slant height of cone can be calculated as follows:

`l = \sqrt{h^{2}+r^{2}}`

`l = \sqrt{12^{2}+3.5^{2}}`

`l = \sqrt{144^{2}+12.25^{2}}`

`l = \sqrt{156.25}` = 12.5 cm


Curved surface area of cone can be calculated as follows:

= `\pi rl`

= `22/7``\times` 3.5 `\times` 12.5

= 137.5 `"cm"^2`


Curved surface area of hemispherical portion can be calculated as follows:

= `2\pi r^2`

= `22/7``\times` 3.5 `\times` 3.5

= 77 `"cm"^2`


Hence, total surface area = 137.5 + 77 = 214.5 `"cm"^2`

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