Analysis and Approaches for IBDP Maths Ebook 1 | Page 142

Your Practice Set – Analysis and Approaches for IBDP Mathematics
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
3
height of the cylinder is 40 m and the volume of the building is 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]
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