Lesson 7 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.

$(- 3, 5) (- 3, - 7)$ :
$(5, - 7) (- 3, - 7)$ :
$(- 3, 5) (5, - 7)$ :

2.

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

$(- 2, - 1) (- 2, - 7)$ :
$(- 6, - 7) (- 2, - 7)$ :
$(- 2, - 1) (- 6, - 7)$ :

3.

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

Set

Volume Formulas
rectangular prism: $V = l \times w \times h$ pyramid: $V = \frac{l w h}{3}$ cylinder: $V = π r^{2} h$ cone: $V = \frac{π r^{2} h}{3}$

Volume Formulas

rectangular prism: $V = l \times w \times h$

pyramid: $V = \frac{l w h}{3}$

cylinder: $V = π r^{2} h$

cone: $V = \frac{π r^{2} h}{3}$

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 $3 ft \times 4 ft \times 2 ft$ .

a.

How much marble (in ${ft}^{3}$ ) 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 $3$ . 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 $6$ pyramids tightly. Give the minimum dimensions of the box. Write a mathematical statement that shows how the volume of the $6$ 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 $6 inches$ and a height of $10 inches$ . The bucket has an $8 -inch$ diameter and a height of $8 inches$ . The cost of the cone of popcorn is $$ 3.50$ . The bucket of popcorn costs $$ 10.00$ . Is the price of the bucket reasonable and fair? Justify your answer.

Go

Find the degree measure of angle $A$ .

Lesson 7 Footprints in the Sand Solidify Understanding

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