Apps. and Interpretation for IBDP Maths Ebook 1 | Page 185

Exercise 49
1. A church is built in the shape of a cylinder with a roof in the shape of a circular cone on
the top. The height of the cylinder is 5 m and its radius is 12 m. The height of the circular
cone is 16 m.
(a)
Calculate the volume of the church.
The roof on the top of the church is to be painted.
[4]
14
(b)
Calculate the area that is to be painted.
[3]
2. A kid’s plastic toy consists of a hemisphere attached to a circular cone with the same base
radius. The height and the radius of the cone are 6 cm and 8 cm respectively.
(a)
(b)
Calculate the volume of the toy.
Calculate the total surface area of the toy.
[4]
[3]
3. A building is built in the shape of a cylinder with a hemispherical roof on the top. The
height of the cylinder is 40 m and the volume of the building is
3
54000� m .
(a)
Calculate the radius of the cylinder.
The hemispherical roof is to be painted.
[5]
(b)
Calculate the area that is to be painted.
[2]
4. A tablet produced has a shape of a cylinder with an identical hemisphere at each end of
the cylinder. The height of the cylinder is 3 mm and the total surface area of the tablet is
2
28� mm .
(a)
(b)
Calculate the radius of the cylinder.
Calculate the volume of the tablet.
[5]
[2]
175
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