Lesson 2 Footprints in the Sand Solidify Understanding

Ready

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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A blank graph. x–5–5–5555y–5–5–5555101010000

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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A blank graph. x–10–10–10–5–5–5555101010y–10–10–10–5–5–5555101010000

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.

A rectangular pyramid of base sides 3ft and 4ft and height of 2 ft.

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.

A rectangular pyramid of base sides 5cm and 5 cm and height of 2.5cm.

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.

A cone with height 10 inches and diameter of 6 inches. Cylinder with height 8 inches and diameter 8 inches.

Go

Find the degree measure of angle .

9.

Triangle ABC with AC = 15, BC = 10, and AB = ? AB is the hypotenuse.

10.

Triangle ABC with AC = 7, BC = ?, and AB = 25 AB is the hypotenuse.

11.

Triangle ABC with AC = ?, BC = 17, and AB = 37 AB is the hypotenuse.

12.

Triangle ABC with AC = ?, BC = 88, and AB = 153 AB is the hypotenuse.

13.

Triangle ABC with AC = 18, BC = ?, and AB = 203 AB is the hypotenuse.

14.

Triangle ABC with AC = 27, BC = 45, and AB = ? AB is the hypotenuse.

15.

Triangle ABC with AC = 23, BC = 4, and AB = ? AB is the hypotenuse.