Geometry Enriched
Study Guide - Chapter 10 Spatial Reasoning
Right Prism
Right Cylinder
Lateral Area (L)
Ph
2π rh
Surface Area
L + 2B
L + 2π r 2
Volume
(right, oblique &
non-regular)
Bh
π r 2h
Regular Pyramid
1
2
Sphere
π r
-----
L + πr2
4π r 2
P
L+B
1
3
Right Cone
Bh
1
3
π r 2h
4
3
πr3
Vocabulary
face - the flat surface of a 3D figure
edge - the segment that is the intersection of two faces
lateral face - a face which is not a base
net - a diagram of the surfaces of a 3D figure that can be folded to form the figure
cross-section - the intersection of a 3D figure and a plane
surface area - the total area of all faces and curved surfaces of a 3D figure
lateral area - the sum of the lateral face areas
prism - formed by two parallel congruent polygonal bases connected by parallelogram faces
base of prism - a face of a prism which is congruent and parallel to another face of the
same prism
right prism - a prism in which all lateral faces are rectangles
oblique prism - a prism in which at least one face is not rectangular
cylinder - formed by two parallel congruent circular bases connected by a curved surface
base of cylinder - one circular face of a cylinder
axis of a cylinder - the segment which connects the centers of the cylinder bases
right cylinder - a cylinder in which the axis is perpendicular to the base
oblique cylinder - a cylinder in which the axis is not perpendicular to the base
pyramid - formed by a polygonal base with triangular faces that connect the base to a vertex
regular pyramid - a pyramid in which the base is a regular polygon and the lateral faces are
congruent isosceles triangles
non-regular pyramid - a pyramid in which the lateral triangular faces are not congruent
slant height l of a pyramid - distance from the vertex to the midpoint of a base edge
altitude - distance from the top vertex to the plane containing the base
cone - formed by a circular base with a curved surface that connects the base to a vertex
slant height l of a cone - distance from the vertex to the base edge of a cone
axis of a cone - the segment which connects the cone’s vertex to the center of the base
right cone - a cone in which the axis is perpendicular to the base
oblique cone - a cone in which the axis is not perpendicular to the base
sphere - a locus of points in space equidistant from a fixed
point
hemisphere - half of a sphere
great circle - divides a sphere into two hemispheres
Net of triangular prism
Geometry Enriched!
Chapters 10 Review Problems!
Name ________________________________
Date ____________________ Period ______
1) Find the volume and surface area of the composite
figure below.
2) A square pyramid has a slant height of 17 cm and a
lateral area of 544 sq cm. What is the volume?
3) Find the volume of a sphere with surface area 196π km
square. Keep in terms of π.
4) In the cube figure, find the diagonal length d when e=3.
5) The length of a right rectangular prism is twice the
width, and the height is three times the width. If the
volume is 162 cm cubed, find the total surface area of the
solid.
6) Find the volume of a regular hexagonal pyramid with
height 8 cm and base edges 6 cm.
7) A solid metal cylinder with radius 6 cm and height 18
cm is melted down and recast as a solid cone with radius
9 cm. Find the height of the cone.
8) A hemispheric bowl with radius 25 contains water
whose depth is 10. What is the area of the water’s
surface?