Algebra & Analytic Geometry
3D Solids – Prisms and Cylinders
Name & Date
1) Consider the square prism below to complete the following.
A) Find the area of the 2 bases.
B) Find the area of the lateral faces (lateral area).
C) Find the total surface area.
D) Find the volume of the solid.
Prisms and Cylinders:
2) Consider the solid below to complete the following.
A) Name the figure
B) Find the area of the 2 bases.
C) Find the area of the lateral faces (lateral area).
D) Find the total surface area.
E) Find the volume of the solid.
3) Consider the solid below to complete the following.
A) Name the figure
B) Find the area of the 2 bases.
C) Find the area of the lateral faces (lateral area).
D) Find the total surface area.
E) Find the volume of the solid.
Algebra & Analytic Geometry
3D Solids – Prisms and Cylinders
Name & Date
4) The cylinder pictured to the right has a circular base with a circumference of 22 cm and a height of 18cm.
A) Find the exact area of the 2 bases.
B) Find the exact area of the lateral faces (lateral area).
C) Find the exact total surface area.
D) Find the exact volume of the solid.
5) The prism below has a regular hexagonal base with a perimeter of 72in and a height of 10in.
A) Find the exact area of the 2 bases.
B) Find the exact area of the lateral faces (lateral area).
C) Find the exact total surface area.
D) Find the exact volume of the solid.
6) Consider the rectangular prism below to complete the following.
A) Find the total surface area.
B) Find the total volume.
7) The swimming below has a regular decagonal base with a perimeter of 35ft and a depth of 60in.
A) Find the cost to produce the pool if the aluminum needed for the outside walls is $1.25 per square foot.
B) If 1 cubic foot = 7.5 gallons, find the total capacity
of the swimming pool.
Algebra & Analytic Geometry
3D Solids – Prisms and Cylinders
Name & Date
8) The diagram of a flower tray below is a Right Trapezoidal Prism in which the bases are Isosceles Trapezoids.
A) Find the combined area of all of the faces of the flower tray. The tray does not have a top.
B) Find the cost to produce the flower tray if the clay used will cost $1.25 per square foot.
C) Find the total volume of the flower tray.
D) If Home Depot sells potting soil for $2 per cubic foot, find the cost to fill the flower tray to the
top.
9) A cube has 2 faces painted black and the remaining faces painted white. The total area of the white faces
is 64 square inches. What is the volume of the cube, in cubic inches?
10) The right circular cylinder below has diameter d and height h. Of the following expressions, which
represents the volume of the smallest rectangular box that completely contains the cylinder?
A)
dh
B)
d 2h
C)
dh 2
D)
d 2h 2
E)
(d  h )2
11) A cube with a volume of 8 cubic centimeters is inscribed in a sphere so that each vertex of the cube
touches the sphere. What is the length of the diameter, in centimeters, of the sphere?
12) How many cubical blocks, each with edges of length 4 centimeters, are needed to fill a rectangular box that
has inside dimensions 20 centimeters by 24 centimeters by 32 centimeters?
13) If the volume of a cube is 8, what is the shortest distance from the center of the cube to the base of the
cube?
14) The three-dimensional figure represented below consists of rectangular and triangular faces. Each
rectangular face has area r and each triangular face has area t. What is the total surface area of the figure in
terms of r and t ?