# Lesson 7Footprints in the SandSolidify Understanding

### 1.

Plot each pair of points on the coordinate grid. Then find the length of the line segment that connects each pair of points.

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### 2.

Plot each pair of points on the coordinate grid. Then find the length of the line segment that connects each pair of points.

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### 3.

What made the third length in problems 1 and 2 more difficult than the others?

## Set

Volume Formulas

rectangular prism:

pyramid:

cylinder:

cone:

### 4.

A marble pyramid with dimensions as shown was sculpted from a marble block. Find the volume.

### 5.

The pyramid shown in problem 4 was chiseled from a block of marble with the dimensions .

#### a.

How much marble (in ) was chiseled away?

#### b.

What fraction of the marble block was discarded?

### 6.

A decorator for a resort ordered a bigger pyramid similar to the pyramid in problem 4, but scaled up by a factor of . Find the volume of the new sculpture.

### 7.

The Crystal Wizard Gift Shop and Meditation Center sells miniature crystal pyramids with dimensions as shown. Design a packing box that will hold pyramids tightly. Give the minimum dimensions of the box. Write a mathematical statement that shows how the volume of the pyramids will fit into the volume of the box.

### 8.

A movie theater sells buttered popcorn in a cone and in a bucket. The cone has a diameter of and a height of . The bucket has an diameter and a height of . The cost of the cone of popcorn is . The bucket of popcorn costs . Is the price of the bucket reasonable and fair? Justify your answer.

## Go

Find the degree measure of angle .