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# A toy is in the shape of a right circular cylinder with a hemisphere on one end and a cone on the other. The radius and height of the cylindrical parts are 5cm and 13 cm, respectively. The radii of the hemispherical and conical parts are the same as that of the cylindrical part. Find the surface area of the toy if the total height of the toy is 30 cm.

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In this question we have to find the surface area
of toy if thetotal height of the toy is 30 cm the
A toy is in the shape of a right circular cylinder
with ahemisphere on one end and a cone on the other.
The radius and height of the cylindrical parts
are 5cm and 13 cm, respectively. The radii of
the hemispherical and conical parts are the same
as that of the cylindrical part. Find

This question is from r d sharma class 10 maths.
I found this question while doing maths class 10.
I need help in getting the solution.

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1. Given,

Height of the Cylindrical portion (H) = 13 cm

Radius of the Cylindrical portion (r) = 5 cm

Height of the whole solid = 30 cm

Then,

The curved surface area of the cylinder (S1) = 2πrh

S1 = 2π(5)(13)

S1 = 408.2 cm2

Let, ‘L’ be the slant height of the cone

And, the curved surface area of the cone (S2) = πrL

S2 = π(6)L

For conical part, we have

h = 30 – 13 – 5 = 12 cm

Then, we know that

L2 = r2 + h2

L2 = 52 + 122

L2 = 25 + 144

L2 = 169

L = 13 m

So,

S2 = π(5)(13) cm2

S2 = 204.28 cm2

Now, the curved surface area of the hemisphere (S3) = 2πr2

S3 = 2π(5)2

S3 = 157.14 cm2

Thus, the total curved surface area (S) = S1 + S2 + S3

S = (408.2 + 204.28 + 157.14)

S = 769.62 cm2

Therefore, the surface area of the toy is 770 cm2

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