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A toy is in the form of a cone of base radius 3.5 cm mounted on a hemisphere of base diameter 7 cm. If the total height of the toy is 15.5 cm, find the total surface area of the top (Use π = 22/7) - Mathematics

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A toy is in the form of a cone of base radius 3.5 cm mounted on a hemisphere of base diameter 7 cm. If the total height of the toy is 15.5 cm, find the total surface area of the top (Use π = 22/7)

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Solution

Let r and h be the radius and height of the cone mounted on the hemisphere, respectively.

Suppose R be the radius of the hemishpere.

Now,

r = R = 3.5 cm

Height of the cone + Radius of the hemisphere = Total height of the toy

h + 3.5 cm = 15.5 cm

h = 15.5 − 3.5 = 12 cm

Let l be the slant height of the cone.

l2=r2+h2

`=>l^2=(7/2)^2+(12)^2=49/4+144=625/4`

`=>l = 25/2cm`

Total surface area of the toy

= Curved surface area of the cone + Curved surface area of the hemisphere

=πrl+2πr2

=πr(l+2r)

`=22/7xx7/2xx(25/2+2xx7/2)`

`=22/7xx7/2xx39/2`

=214.5 cm2

Concept: Surface Area of a Combination of Solids
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