Lesson 12

Prisms and Pyramids

  • Let’s describe relationships between pyramids and prisms.

Problem 1

Give each solid a geometric name. Be as precise as you can.


7 sided solid. Hexagon with 6 rectangles meeting on the left side of the solid.


5 sided solid. Two right triangles and 3 rectangles.


An oblique cone, no units labeled. A dotted line representing the height of the cone is drawn perpendicular to the plane in which the base lies.

Problem 2

Each set of two-dimensional shapes is the complete list of faces from a particular solid. Match each set of shapes with the solid they came from.

Problem 3

These 3 congruent square pyramids can be assembled into a cube with side length 1 foot. What is the volume of each pyramid?

Rectangular pyramid 
Rectangular pyramid 
Rectangular pyramid 

Problem 4

A prism has a height of 4 inches and a volume of 120 cubic inches. Select all figures that could be the base for this prism.


a 5 inch by 6 inch rectangle


a square with side length 5 inches


a circle with radius 5 inches


a star-shaped base with area 30 square inches


a right triangle with legs 5 inches and 12 inches

(From Unit 5, Lesson 11.)

Problem 5

This prism has a right triangle for a base. The volume of the prism is 54 cubic units. What is the value of \(h\)?

Prism with base that is triangle A, B C. Angle A, C B is a right angle. C A, length 4. A, B length 5. Second base triangle D E F, Angle D F E is a right angle. C F, length h.
(From Unit 5, Lesson 11.)

Problem 6

This solid has curved sides. All cross sections parallel to the base are squares measuring 3 units on each side. The height from the base to the top is 5 units. What is the volume of this solid?

Solid with curved sides. Top and bottom bases are squares, side lengths = 3.
(From Unit 5, Lesson 10.)

Problem 7

Find the volume of each solid.

  1. a cylinder with radius 3 inches and height 2 inches
  2. a hexagonal prism whose base has area 4.5 square centimeters and whose height is 7 centimeters
  3. a prism 5 feet tall whose base is a right triangle with leg lengths \(\frac32\) feet and 9 feet
(From Unit 5, Lesson 9.)

Problem 8

A circle with area \(\pi\) square units is dilated using a scale factor of 5. What is the area of the dilated circle?

(From Unit 5, Lesson 4.)