# 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.

### 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?

### 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

### 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 \(h\)?

### 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?

### Problem 7

Find the volume of each solid.

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

### 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?