Geometry CC
HW 11.6
Name _______________________________
Period _______
1.
Find the volume of the prism below:
2.
The volume of the prism below is 240u 3 . Find the height of the prism.
3.
Use the principle of parallel slices to show that the three triangles shown below all
have the same area.
Figure 1
Figure 2
Figure 3
4.
An oblique circular cylinder has height 5 and volume 45𝜋. Find the radius of the
circular base.
5.
An oblique prism has a rectangular base that is 16 in. × 9 in. A hole in the prism is
also the shape of an oblique prism with a rectangular base that is 3 in. wide and 6 in.
long, and the prism’s height is 9 in. (as shown in the diagram). Find the volume of
the remaining solid.
6.
A right circular cone and a solid hemisphere share the same base. The vertex of the
cone lies on the hemisphere. Removing the cone from the solid hemisphere forms a
solid. Draw a picture, and describe the cross-sections of this solid that are parallel
to the base.
7. Use Cavalieri’s principle to explain why a circular cylinder with a base of radius 5 and a
height of 10 has the same volume as a square prism whose base is a square with edge
length 5√𝜋 and whose height is also 10.
8.
In the figure below we have two tetrahedrons ABCD and PQRS such that base
triangles ABC and PQR have same area. Also the height of both tetrahedrons is same
i.e. the distance of point D from plane of ABC is same as that of point S from plane of
PQR. If triangle A’B’C’ and triangle P’Q’R’ are both cross sections that are half way
between the base and vertices D and S respectively, what can be said about triangles
A’B’C’ and P’Q’R’?
9. In the parallelepiped, to the left. The length of AB is 2x, the length of GM is x + 3, and the
width is 6. What is the volume of this figure in terms of x?
G
A
M
B