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Question
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
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