which of the following is the area of the largest circles that can fit entirely inside a rectangle that measures 8 centimeters by 10 centimeters

ATI TEAS 7

TEAS Practice Test Math

1. What is the area of the largest circle that can fit entirely inside a rectangle that measures 8 centimeters by 10 centimeters?

A. 18π cm²
B. 10π cm²
C. 16π cm²
D. 8π cm²

Correct answer: C

Rationale: The largest circle that can fit inside the rectangle would have a diameter of 8 cm, which means the radius is half of the diameter, thus 4 cm. The area of a circle is calculated using the formula A = πr², where r is the radius. Substituting the radius value into the formula, the area of the circle is π(4)² = 16π cm². Therefore, the correct answer is 16π cm². Choice A (18π cm²), B (10π cm²), and D (8π cm²) are incorrect because they do not represent the area of the largest circle that fits inside the given rectangle.

2. What percentage of the total rainfall in this timeframe occurs during October?

A. 0.135
B. 0.151
C. 0.169
D. 0.177

Correct answer: B

Rationale: To calculate the percentage of rainfall that occurs during October, divide October's rainfall (4.5 inches) by the total rainfall (29.38 inches) and multiply by 100. So, (4.5 / 29.38) * 100 = 15.31%. Among the choices given, option B, 0.151, is the closest to this calculated percentage. Options A, C, and D are not correct as they do not match the accurate calculation based on the provided data.

3. A new physician saw 841 clients during the first year of practice and 1072 clients during the second year of practice. Which of the following represents the approximate percentage increase in client volume?

A. 22%
B. 27%
C. 127%
D. 78%

Correct answer: B

Rationale: To calculate the percentage increase, subtract the initial value from the final value, then divide by the initial value and multiply by 100. In this case, the calculation is ((1072 - 841) / 841) x 100 ≈ 27%. Therefore, the correct answer is B. Choice A (22%) is incorrect as it does not match the calculated percentage increase. Choice C (127%) is incorrect as it represents an absolute increase, not a percentage increase. Choice D (78%) is incorrect as it is not close to the calculated percentage increase of 27%.

4. Arrange the following numbers from least to greatest: 7/3, 9/2, 10/9, 7/8

A. 10/9, 7/3, 9/2, 7/8
B. 9/2, 7/3, 10/9, 7/8
C. 7/3, 9/2, 10/9, 7/8
D. 7/8, 10/9, 7/3, 9/2

Correct answer: D

Rationale: To arrange the numbers from least to greatest, first convert them to decimals: 1. 7/3 is approximately 2.33 2. 9/2 equals 4.5 3. 10/9 is approximately 1.11 4. 7/8 equals 0.875 Now, arrange the decimals from least to greatest: 0.875 (7/8), 1.11 (10/9), 2.33 (7/3), 4.5 (9/2). Therefore, the correct order is 7/8, 10/9, 7/3, 9/2. Choice A is incorrect because it doesn't follow the correct order. Choice B is incorrect as it places 9/2 before 7/3, which is not the right arrangement. Choice C is incorrect as it places 7/3 before 9/2 and 10/9, which is incorrect. Thus, the correct answer is choice D.

5. Which decimal is the smallest?

A. 2.22
B. 2.02
C. 2.002
D. 2.2

Correct answer: C

Rationale: To determine the smallest decimal, we look at the digits after the decimal point. In this case, 2.002 is the smallest because it has the least value in the thousandths place. Choice A, 2.22, has a higher value in the hundredths place making it larger. Choice B, 2.02, has a higher value in the hundredths place compared to 2.002. Choice D, 2.2, is larger than 2.002 as it has a higher value in the tenths place.