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# A 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 to - Mathematics

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#### Questions

A 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 [Use π =22/7]

A toy is in the form of a cone of radius 3.5 cm mounted on a hemisphere of same radius on its circular face. The total height of the toy is 15.5 cm. Find the total surface area of the toy

#### Solution

Radius of hemisphere = 3.5 cm

Total height of the toy = 15.5 cm.

Surface area of cone

=pirl

l = sqrt((12)^2 + (3.5)^2)

= sqrt156.25

=12.5 cm

Therefore,

Surface area of cone

= 22/7 xx 3.5 xx 12.5

=137.5 cm^2

Surface area of hemisphere

=2pir^2

= 2 xx 22/7 xx 3.5 xx 3.5

= 77 cm^2

Therefore,

Total surface area of the toy

=137.5 + 77

=214.5 cm^2

Volume of cone

=1/3pir^2h

=1/3 xx 22/7 xx (3.51^2 xx 12)

=154 cm^2

Volume of hemisphere

=2/3pir^3

= 2/3 xx 22/7 xx (3.5)^3

= 89.83 cm

Therefore,

Total volume of the toy

= (154 + 89.83) cm^3

= 243.83 cm^3

Is there an error in this question or solution?

#### APPEARS IN

NCERT Solution for Mathematics Textbook for Class 10 (2019 (Latest))
Chapter 13: Surface Areas and Volumes
Ex. 13.1 | Q: 3 | Page no. 244
RD Sharma Solution for Class 10 Maths (2018 (Latest))
Chapter 14: Surface Areas and Volumes
Q: 47 | Page no. 83
RD Sharma Solution for Class 10 Maths (2018 (Latest))
Chapter 14: Surface Areas and Volumes
Q: 47 | Page no. 83

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Solution A 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 to Concept: Surface Area of a Combination of Solids.
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