A toy is in the combined form of a cylinder and a cone having the equal base

whose diameter is 10 cm. The length of the cylindrical part is 14 cm and

height of the cone is 12 cm of that toy. If the measurement of diameter and

height of the cone are interchanged and formed the next similar toy, find

which toy costs more for the painting at the same rate for per square

centimeter.

# A toy is in the combined form of a cylinder and a cone having the equal base

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Answer:Height of cylinder =40cm=h

Radius of cone, hemisphere =3cm=r

Height of cone =40cm=h

Total surface area of toy = surface area of hemisphere + surface are of cylinder + surface area of cone.

=2πr

2

+2πrh+πrl

l

2

=r

2

+h

2

=3

2

+4

2

=9+16=25

l

2

=25⇒l=

25

=5cm

Curved surface area of hemisphere =2πr

2

=2×

7

22

×3

2

=56.57cm

2

Curved surface area of cylinder =2πrh

=2(

7

22

)×3×40

=754.28cm

2

Curved surface area of cone =πrl

=

7

22

×3×5

=47.14cm

2

∴ Total surface area of toy =56.57cm

2

+754.28cm

2

+47.14cm

2

=(56.57+47.14+754.28)cm

2

=857.99cm

2

.