Analysis and Approaches for IBDP Maths Ebook 1 | Page 150

Your Practice Set – Analysis and Approaches for IBDP Mathematics
(a) Find the size of angle OVA .
[2]
(b) Find the total surface area of the cone.
[3]
(c) Find the volume of the cone.
[4]
The cone is cut into two parts horizontally such that the two parts have the same volume.
The upper part is a smaller cone and the lower part is a frustum. Let R and H be the
base radius and the vertical height of the upper part respectively.
(d) Express R in terms of H .
(e) Find the value of H and of R .
[2]
[6]
4. A square pyramid VABCD has a vertical height VO of 56 cm and a slant height VA of
70 cm, where O is the centre of the base, shown in the following diagram.
(a) Find the size of angle OVA .
(b) Find the length of AD .
(c)
Find the volume of the cone.
The pyramid is cut into two parts horizontally such that the two parts have the same
volume. The upper part is a smaller pyramid and the lower part is a frustum. Let x cm
and
2
y cm be the base area of the upper part and the area of the square ABCD
respectively. It is given that the vertical height of the upper part is
1
�
3
56� 2 cm .
2
[2]
[4]
[3]
(d) Find x:
y giving the answer in the form 1:n .
[6]
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