Lesson 3 Take Another Spin Solidify Understanding

Ready

For problems 1–3, use the two spinners with equal-sized sections.

Circle with three sectors, blue, orange, and red. Circle with five sectors, green, pink, gray, purple, brown. redblueorangepurplegreenpinkbrowngray

1.

Create a representation of the sample space created by spinning the first spinner followed by spinning the second spinner.

2.

Find the probability of the first spinner landing on blue and the second spinner landing on green.

3.

Find the probability of the first spinner landing on red and the second spinner landing on brown or gray.

For problems 4–6, four different colored marbles were pulled from a paper bag. The color of the marble was recorded, and then the marble was put back into the bag. There are marbles in the bag and the data for the color of the marble chosen is provided in the table.

Marble Color

Frequency of Selection

blue

green

red

yellow

4.

What is the probability of selecting a green marble?

5.

What is the probability of selecting a red marble?

6.

Based on the frequency that each marble was selected, how many of each color of marble would you predict are actually in the bag?

Set

The picture shown is of the Washington Monument in Washington, DC. The shaft of the monument is a square frustum. The bottom square measures on a side, and the top square measures . The top is a square pyramid.

an image of the Washington monument

7.

Find the length of the sides and the altitude of the triangular faces of the pyramid.

(Height of pyramid is )

square pyramid; base of side 34.5 ft and height of 55.5 ft. 34.5 ft34.5 ft55.5 ft

8.

Find the area of each face of the pyramid.

9.

Find the area of the trapezoids that make the faces of the frustum. The area of a trapezoid:

Trapezoid with base 55 ft, top 34.5 ft, and height 500 ft.

10.

Find the total surface area of the Washington Monument.

11.

Find the total volume of the Washington Monument.

Volume of a square frustum: where and are the side lengths of each square.

Volume of pyramid:

12.

Draw a sketch of the 3-D object formed by rotating the figure about the -axis.

rectangular with trapezoid shape missing 222444000

Go

Use the given information and what you know about triangles to find the measure of the missing angles in the triangles.

13.

Triangle RST with ST and TR congruent and angle T =124 124°

14.

Triangle ABC with angle C 90 degrees and angle B 60 degrees 60°

15.

Equilateral Triangle EFG

16.

Triangle PQR with angle P 46 degrees and exterior angle Q 78 degrees

17.

Triangle RST with angle T 119 degrees and exterior angle R 146 degrees

18.

Triangle EFH with angle E a right angle, Triangle FGH. Line segment FG and EH parallel. Line segment GH and FE parallel.

19.

Triangle GHK

20.

Triangle LMN; Angle N =x 3, Angle L=2x 5, Angle M=3x-2