Lesson 6 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.

A right triangle with one side 10, hypotenuse ?, and one side 24

2.

A right triangle with one side 20, hypotenuse 50, and one side ?

3.

A right triangle with one side 16, hypotenuse ?, and one side 16

4.

An equilateral Triangle with sides 28 and altitude ?

5.

A square with sides of 28 and diagonal ?

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.

Rectangular prism labeled Laundry Detergent with sides 3 in, and 14 in, and 10 in.
Rectangular prism labeled Laundry Detergent with sides 6 in, and 8 in, and 9 in.

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?

Rectangular prism labeled Brand A Hot Cocoa Mix with sides of 7 inches. Cylinder labeled Brand B Cocoa Mix, height 7 in and diameter 8 in Brand AHot Cocoa MixBrand BCocoa Mix

8.

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

Rectangular Prism with sides 16 cm, 6 cm, and 15 cm.

9.

A large order is placed with the distribution company in problem 8 for a container that has a capacity of . The company has a similar container that is larger than the one in problem 8 by a scale factor of . Will the larger container be big enough to contain ? 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 . Compare the volume of the flour cannister to the volume of the sugar cannister.

Flour cannister height 9 in and diameter 20 in. Sugar cannister FlourSugar

Go

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

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Change the measure of the given angle to degrees.

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