Question

A toy is in the shape of a right circular cylinder with a hemisphere on one end and a cone on the other. The height and radius of the cylindrical part are 13cm and 5cm respectively. The radii of the hemispherical and conical parts are the same as that of the cylindrical part. Calculate the volume of the toy if the height of the conical part is 12cm.

Answer 1

Answer:

Let r cm be the radius and h cm the height of the cylindrical part. Then, r=5cm,h=13cm

Clearly radii of the spherical part and base of the conical part are also r cm. Let h

1

cm be the height, l cm be the slant height of the conical part.

Then

l

2

=r

2

+h

1

2

⇒l=

r

2

+h

1

2

⇒l=

5

2

+12

2

=13cm

Now

surface area of the toy=

curved surface area of the cylindrical part + curved surface area of hemispherical part + curved surface area of conical part

=(2πrh+2πr

2

+πrl)cm

2

=πr(2h+2r+l)cm

2

={

7

22

×5×(2×13+2×5+13)}cm

2

=770cm

2