Apps. and Interpretation for IBDP Maths Ebook 1 | Page 192

Your Practice Set – Applications and Interpretation for IBDP Mathematics
Exercise 52
1. A solid metal hemisphere has a base radius of 10 cm.
(a) Find the volume of the hemisphere.
[3]
(b) Find the total surface area of the hemisphere.
[3]
Four identical hemispheres were melted and recast into a solid circular cone, shown in the
following diagram. The base diameter AB is 38 cm.
(c) Find the value of the height, OV , of the cone.
(d) Find the size of angle AVB .
(e) Find the total surface area of the cone.
[3]
[4]
[3]
2. A solid pentagonal prism has a base area of
perimeter of the pentagonal base is 62 cm.
2
260 cm and a height of 100 cm. The
(a) Find the volume of the prism.
[2]
(b) Find the total surface area of the prism.
[3]
The prism was melted and recast into a solid square pyramid VABCD , shown in the
following diagram. O is the centre of the base. The vertical height OV is 40 cm. M is
the mid-point of AD .
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