# Lesson 14

Working with Pyramids

### Problem 1

A pyramid has a height of 5 inches and a volume of 60 cubic inches. Select all figures that could be the base for this pyramid.

A:

a square with side length 6 inches

B:

a 3 inch by 4 inch rectangle

C:

a 4 inch by 9 inch rectangle

D:

a circle with radius 4 inches

E:

a right triangle with one side 5 inches and the hypotenuse 13 inches

F:

a hexagon with an area of 36 square inches

### Problem 2

A company makes a block of cheese in the shape of a rectangular prism with dimensions 4 inches by 2 inches by 2 inches. They want to make a new block, in the shape of a rectangular pyramid, that uses the same amount of cheese. Determine two sets of possible dimensions for the pyramid.

### Problem 3

Select all the solids with volume 40 cubic units.

A:

Solid A

B:

Solid B

C:

Solid C

D:

Solid D

E:

Solid E

F:

Solid F

### Problem 4

The volume of a pyramid is 50 cubic units. The base is a square with sides of length 5. What is the height?

A:

2 units

B:

4 units

C:

6 units

D:

10 units

### Solution

(From Unit 5, Lesson 13.)

### Problem 5

A cone and a cylinder have the same radius and height. The volume of the cone is $$100\pi$$ cubic feet. What is the volume of the cylinder?

### Solution

(From Unit 5, Lesson 13.)

### Problem 6

A solid can be constructed with 2 congruent triangles and 3 rectangles. What is the name of this solid?

A:

right triangular pyramid

B:

right triangular prism

C:

square pyramid

D:

rectangular prism

### Solution

(From Unit 5, Lesson 12.)

### Problem 7

An oblique cylinder with a base of radius 3 is shown.

The top of the cylinder can be obtained by translating the base by the directed line segment $$AB$$ which has length $$6\sqrt{2}$$. The segment $$AB$$ forms a $$45^\circ$$ angle with the plane of the base. What is the volume of the cylinder?

A:

$$18\pi$$ cubic units

B:

$$18\pi\sqrt{2}$$ cubic units

C:

$$36\pi$$ cubic units

D:

$$54\pi$$ cubic units