Lesson 1 Sand Castles Solidify Understanding

Ready

Find the exact value of the indicated lengths.

(The triangles in problems 1, 2, and 3 are right triangles.)

1.

2.

3.

4.

5.

Set

6.

In 1946, a miracle cleaning product was launched in the United States. It was granular laundry detergent instead of bar soap. For almost 20 years after 1946, laundry detergent came in a box shaped much like a box of cereal.

In the late 1960s, the shape of the box changed so that it would fit better on a shelf. No one wanted to buy the new detergent because it was the same price but the box looked much smaller.

Prove to consumers that the new box was actually a better bargain.

7.

Brand A of powdered hot cocoa mix is packaged in a rectangular box. Brand B is packaged in a cylindrical container. Both brands sell for the same price. Which brand is the better deal?

8.

A distribution company uses a small packing container, as shown in the figure. Find the volume.

9.

A large order is placed with the distribution company in problem 8 for a container that has a capacity of ${38,500 cm}^{3}$ . The company has a similar container that is larger than the one in problem 8 by a scale factor of $3$ . Will the larger container be big enough to contain ${38,500 cm}^{3}$ ? Justify your answer.

10.

A cannister for storing flour has the dimensions shown. A similar cannister for storing sugar has been scaled down by a factor of $\frac{1}{2}$ . Compare the volume of the flour cannister to the volume of the sugar cannister.

Go

Change the measure of the given angle to radian measure. Leave $π$ in your answers.

11.

$120 °$

12.

$270 °$

13.

$210 °$

14.

$300 °$

15.

$180 °$

16.

$90 °$

Change the measure of the given angle to degrees.

17.

$\frac{3 π}{4}$

18.

$\frac{π}{6}$

19.

$\frac{2 π}{5}$

20.

$\frac{π}{12}$

21.

$4.71$

22.

$1.57$