Apps. and Interpretation for IBDP Maths Ebook 1 | Page 187

Exercise 50
1. A metal hemisphere has a radius 22 cm.
(a) Find the volume of the hemisphere expressing your answer in the form a� 10 k ,
1�a
� 10 and k � .
[3]
The hemisphere is to be melted down and remoulded into the shape of a cylinder with a
height of 26 cm.
14
(b)
Find the radius of the base of the cylinder.
[3]
2. A metal square-based pyramid has a height 35 cm and a base length 8� cm .
(a) Find the volume of the pyramid expressing your answer in the form a� 10 k ,
1�a
� 10 and k � .
The pyramid is to be melted down and remoulded into the shape of a sphere.
[3]
(b)
Find the radius of the sphere.
[3]
3. A metal cylinder has a height 100 cm and a radius 7 cm.
(a) Find the volume of the cylinder expressing your answer in terms of � .
[2]
The cylinder is to be melted down and remoulded into ten identical metal hemispheres.
(b) Find the radius of one hemisphere expressing your answer in the form a� 10 k ,
1�a
� 10 and k � .
[4]
4. The radius and the vertical height of a metal circular cone are both equal to 27 cm.
(a) Find the volume of the circular cone expressing your answer in the form a� 10 k ,
1�a
� 10 and k � .
[3]
4 identical circular cones are to be melted down and remoulded into 27 identical metal
spheres.
(b)
Find the ratio of the radius of the cone to the radius of the sphere.
[4]
www.seprodstore.com
177