Math, asked by rasal9995, 8 months ago

toy is in the form of a 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 the toy.

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Answered by EknoorSaini
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Surface Areas and Volumes

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A toy is in the form of a c...

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Asked on December 20, 2019 bySaptarshi Swaraj

A toy is in the form of a cone mounted on a hemisphere of radius 3.5 cm . The total height of the toy is 15.5cm . Find the total surface area and volume of the toy . 

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Given: toy in form of a cone mounted on a hemisphere

radius of hemisphere =3.5 cm

Total height of toy =15.5 cm

To find: Total surface area TSA = ? Volume, V = ?

Solution :

h=12 cm

r=3.5 cm

Assuming that the cone is completed mounted on hemisphere

TSA of toy = CSA of cone + CSA of hemisphere

=πrl+2πr2 [r→ radius of both cone and hemisphere as it is here]

=πr[l+2r]

=722×1035[(12)2+(3.5)2+2×1035]

=11[144+12.25+7]=11[156.25+7]

=11(12.5+7)

=11×19.5

=214.5cm2

Volume of toy = 31πr2h+32

Answered by Anonymous
21

Answer:

We have,

Radius of cone = Radius of hemisphere = 3.5 cm.

Height of the toy = 15.5 cm

To calculate the CSA of cone we have to find first the Slant Height of the cone :]

Slant Height = h² + r²

Slant Height = (15.5)² + (3.5)²

Slant Height = 12.25 + 144

Slant Height = 156.25 cm²

Slant Height = 12.5 cm

Now, we will calculate the TSA of the toy :

➳ TSA of toy = CSA of hemisphere + CSA of cone

➳ TSA of toy = 2πr² + πrl

➳ TSA of toy = 2π(3.5)² + π(3.5)(12.5)

➳ TSA of toy = 24.5π + 43.75π

➳ TSA of toy = 68.25π

➳ TSA of toy = 68.25 * 22/7

➳ TSA of toy = 214.5 cm²

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