Mathematics for Elementary Educators III
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Free Mathematics for Elementary Educators III Questions
Find the volume of a cone with a radius of 4 in and a height of 6 in.
- 66.65 in cubed
- 150.72 in cubed
- 301.44 in cubed
- 100.48 in cubed
Explanation
Correct answer: (D.) 100.48 in cubed
The volume of a cone is calculated using the formula:
V=1/3πr2h
Substitute r = 4 in and h = 6 in:
V = 13π(4)2(6) = ⅓π(16×6) = ⅓π(96) = 32π
Using π ≈ 3.1416:
V ≈ 32 × 3.1416 ≈ 100.53 in3
The closest option is 100.48 in³.
A lottery hopper uses balls numbered 1–50. After each ball is chosen, it is not replaced. Which of the following is the probability that the number 13 is not selected on either of the first two draws?
- 48/50
- 02-Jan
- 2,498/2,500
- 2,352/2,450
Explanation
Correct answer: (A.) 48/50
Omar has a circular table with a diameter of 10 in, and Mei has a square table with each side measuring 10 in. Omar says that his table will require more material to cover, but Mei disagrees and thinks her table will require more material. Who is correct and why?
- Mei, because her table requires 40 in squared of material
- Mei, because her table requires 100 in squared of material
- Omar, because his table requires 314.16 in squared of material
- Omar, because his table requires 31.79 in squared of material
Explanation
Correct answer: (B.) Mei, because her table requires 100 in squared of material
To compare the material needed, calculate the area of each table.
For Omar’s circular table, the radius r = 10/2 = 5 in. The area of a circle is A = πr2:
A = 3.1416 * 52 = 3.1416 * 25 ≈ 78.54 in2.
For Mei’s square table, each side is 10 in, so the area is A = s2 = 102 = 100 in2.
Since 100 in² > 78.54 in², Mei’s table requires more material to cover.
An in-ground pool measures 16 ft by 40 ft and has a 2 ft wide walkway around it. What is the area of the walkway around the pool?
- 880 ft squared
- 116 ft squared
- 640 ft squared
- 240 ft squared
Explanation
Correct answer: (D.) 240 ft squared
To find the area of the walkway, calculate the total area of the pool plus walkway, then subtract the area of the pool.
The pool dimensions are 16 ft by 40 ft. Adding a 2 ft walkway around all sides increases each dimension by 4 ft (2 ft on each side):
Total length = 40 + 4 = 44 ft
Total width = 16 + 4 = 20 ft
The total area including the walkway is:
44 × 20 = 880 ft2
The pool area alone is:
40 × 16 = 640 ft2
The walkway area is the difference:
880 - 640 = 240ft2
The weights in pounds of 14 cats are: 8.8, 10.2, 9.6, 9.1, 10.2, 13.3, 12.6, 8.2, 12.5, 10.4, 11.7, 10.5, 10.9, 10.2. What is the median weight of the cats?
- 10.5
- 10.6
- 10.2
- 10.3
Explanation
Correct answer: (D.) 10.3
First, arrange the weights in ascending order:
8.2, 8.8, 9.1, 9.6, 10.2, 10.2, 10.2, 10.4, 10.5, 10.9, 11.7, 12.5, 12.6, 13.3
There are 14 data points. The median is the average of the 7th and 8th values:
7th value = 10.2, 8th value = 10.4
Median = (10.2 + 10.4)/2 = 10.3
Mathematics for Elementary Educators III (D127)
Question 1.
Which of the following pairs of angles are supplementary? (Choose all that apply.)
- 45 degrees and 45 degrees
- 72 degrees and 100 degrees
- 35 degrees and 55 degrees
- 60 degrees and 120 degrees
Explanation
Correct answer: (D.) 60 degrees and 120 degrees
Supplementary angles are two angles whose measures add up to 180 degrees. Checking each pair: 45 + 45 = 90, which is not supplementary. 72 + 100 = 172, also not 180. 35 + 55 = 90, not supplementary. 60 + 120 = 180, which meets the condition. Therefore, only the pair in option D is supplementary.
A circle has a radius of 4.5 cm. What is the area of the circle?
- 28.26 cm squared
- 31.79 cm squared
- 15.90 cm squared
- 63.59 cm squared
Explanation
Correct answer: (D.) 63.59 cm squared
The area of a circle is calculated using the formula A = πr2, where r is the radius. Substituting r = 4.5 cm:
A =π(4.5)2 = π(20.25) ≈ 63.59 cm2
Thus, the area of the circle is approximately 63.59 cm squared.
A company tracks the number of daily sales for three brands during a given month using the box plots of the data. One of the brands sold out on a given day and could not be restocked, resulting in the lowest single-day sales. Which brand sold out?
- Brand A
- Brand C
- Brand B
- Brands A, B, and C
Explanation
Correct answer: (C.) Brand B
In a box plot, the left whisker shows the minimum value. Brand B has the lowest left whisker among the three brands, indicating it had the lowest single-day sales and therefore sold out.
The diagonal of a rectangle measures 29 in, and the length of the rectangle is 23.2 in. What is the area of this rectangle?
- 504.60 in squared
- 201.84 in squared
- 403.68 in squared
- 372.80 in squared
Explanation
Correct answer: (C.) 403.68 in squared
In a rectangle, the diagonal, length, and width form a right triangle, so we can use the Pythagorean theorem:
diagonal2 = length2 +width2
Substitute the known values:
292 = 23.22 + w2
841 = 538.24 + w2
w2 = 841 - 538.24 = 302.76
w = sqrt(302.76) ≈ 17.4 in
The area of the rectangle is:
Area = length × width = 23.2 × 17.4 ≈ 403.68 in2
A builder cuts a 6 m rope into four pieces. Three of the pieces measure 1.2 m, 1.5 m, and 2.7 m. What is the length of the remaining piece?
- 0.6 m
- 6 m
- 60 m
- 600 m
Explanation
Correct answer: (A.) 0.6 m
To find the remaining piece, subtract the sum of the three known pieces from the total length of the rope:
Remaining length = 6 - (1.2 + 1.5 + 2.7)
1.2 + 1.5 + 2.7 = 5.4
6 - 5.4 = 0.6 m
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