The volume of 1 cup of water is 14.4 cubic inches. The diameter of an empty cylindrical can is 3.0 inches. The can holds 2.0 cups of water. What is the height of the can, to the nearest 0.1 inch?
- A. 1
- B. 2
- C. 3.1
- D. 4.1
- E. 6.2
Correct Answer & Rationale
Correct Answer: D
To find the height of the can, first determine the total volume of water it holds. Since 1 cup is 14.4 cubic inches, 2 cups equal 28.8 cubic inches (2 x 14.4). The formula for the volume of a cylinder is V = πr²h. The radius (r) of the can is half the diameter: 1.5 inches. Plugging in the values: 28.8 = π(1.5)²h. Calculating the area of the base gives approximately 7.07. Rearranging the equation for height (h) results in h ≈ 4.1 inches. Options A (1), B (2), C (3.1), and E (6.2) do not satisfy the volume calculation, as they yield heights inconsistent with the required volume based on the diameter provided.
To find the height of the can, first determine the total volume of water it holds. Since 1 cup is 14.4 cubic inches, 2 cups equal 28.8 cubic inches (2 x 14.4). The formula for the volume of a cylinder is V = πr²h. The radius (r) of the can is half the diameter: 1.5 inches. Plugging in the values: 28.8 = π(1.5)²h. Calculating the area of the base gives approximately 7.07. Rearranging the equation for height (h) results in h ≈ 4.1 inches. Options A (1), B (2), C (3.1), and E (6.2) do not satisfy the volume calculation, as they yield heights inconsistent with the required volume based on the diameter provided.
Other Related Questions
An irrigation pivot makes a circle with a radius of about 400 meters. Which of the following values is closest to the area, in square meters, of the circle?
- A. 1300
- B. 2500
- C. 160000
- D. 502700
- E. 1579100
Correct Answer & Rationale
Correct Answer: D
To find the area of a circle, the formula \( A = \pi r^2 \) is used, where \( r \) is the radius. With a radius of 400 meters, the area calculates to approximately \( A = \pi \times (400)^2 \approx 502700 \) square meters, making option D the closest value. Option A (1300) is far too low, indicating a misunderstanding of the formula. Option B (2500) is also significantly underestimated for such a large radius. Option C (160000) is closer but still incorrect, as it neglects the multiplication by \( \pi \). Option E (1579100) overestimates the area, suggesting a miscalculation of the radius or the area formula.
To find the area of a circle, the formula \( A = \pi r^2 \) is used, where \( r \) is the radius. With a radius of 400 meters, the area calculates to approximately \( A = \pi \times (400)^2 \approx 502700 \) square meters, making option D the closest value. Option A (1300) is far too low, indicating a misunderstanding of the formula. Option B (2500) is also significantly underestimated for such a large radius. Option C (160000) is closer but still incorrect, as it neglects the multiplication by \( \pi \). Option E (1579100) overestimates the area, suggesting a miscalculation of the radius or the area formula.
What are the solutions to (x-2)(x+4) = 0?
- A. -4 and 2
- B. -3 and 1
- C. -2 and 4
- D. -1 and 1
- E. -1 and 3
Correct Answer & Rationale
Correct Answer: A
To solve the equation (x-2)(x+4) = 0, we apply the zero product property, which states that if a product of factors equals zero, at least one of the factors must equal zero. Setting each factor to zero gives us the equations x - 2 = 0 and x + 4 = 0. Solving these yields x = 2 and x = -4, confirming that the solutions are -4 and 2. Options B, C, D, and E provide incorrect pairs of solutions that do not satisfy the original equation when substituted back in. Each of these pairs results in non-zero products for the factors, thus failing to meet the requirement of the equation.
To solve the equation (x-2)(x+4) = 0, we apply the zero product property, which states that if a product of factors equals zero, at least one of the factors must equal zero. Setting each factor to zero gives us the equations x - 2 = 0 and x + 4 = 0. Solving these yields x = 2 and x = -4, confirming that the solutions are -4 and 2. Options B, C, D, and E provide incorrect pairs of solutions that do not satisfy the original equation when substituted back in. Each of these pairs results in non-zero products for the factors, thus failing to meet the requirement of the equation.
Quadrilateral ABCD satisfies the following conditions: Side AB is parallel to side CD, Side BC is not parallel to side AD. Which term is the best classification for quadrilateral ABCD?
- A. Parallelogram
- B. Rectangle
- C. Rhombus
- D. Square
- E. Trapezoid
Correct Answer & Rationale
Correct Answer: E
Quadrilateral ABCD has one pair of parallel sides (AB and CD), which defines it as a trapezoid. Option A, parallelogram, is incorrect because both pairs of opposite sides must be parallel. Option B, rectangle, is a specific type of parallelogram with right angles, so it also requires two pairs of parallel sides. Option C, rhombus, similarly demands both pairs of opposite sides to be parallel, along with equal side lengths. Option D, square, is a special type of rectangle and rhombus, necessitating both pairs of parallel sides and equal side lengths. Thus, the only classification that fits is trapezoid.
Quadrilateral ABCD has one pair of parallel sides (AB and CD), which defines it as a trapezoid. Option A, parallelogram, is incorrect because both pairs of opposite sides must be parallel. Option B, rectangle, is a specific type of parallelogram with right angles, so it also requires two pairs of parallel sides. Option C, rhombus, similarly demands both pairs of opposite sides to be parallel, along with equal side lengths. Option D, square, is a special type of rectangle and rhombus, necessitating both pairs of parallel sides and equal side lengths. Thus, the only classification that fits is trapezoid.
Jasmine’s pace for a 3-mile race is 1 minute per mile faster than her pace for a 13-mile race. She ran the 3-mile race in 21 minutes. How many minutes will it take her to run the 13-mile race?
- A. 34
- B. 78
- C. 92
- D. 101
- E. 104
Correct Answer & Rationale
Correct Answer: E
Jasmine completed the 3-mile race in 21 minutes, which gives her a pace of 7 minutes per mile (21 minutes ÷ 3 miles). Since her pace for the 13-mile race is 1 minute slower, her pace for that race is 8 minutes per mile. To find the time for the 13-mile race, multiply her 13-mile pace by the distance: 8 minutes/mile × 13 miles = 104 minutes. Options A (34), B (78), C (92), and D (101) all reflect incorrect calculations or misunderstandings of her pacing difference and distance, leading to values that do not align with the established pace of 8 minutes per mile.
Jasmine completed the 3-mile race in 21 minutes, which gives her a pace of 7 minutes per mile (21 minutes ÷ 3 miles). Since her pace for the 13-mile race is 1 minute slower, her pace for that race is 8 minutes per mile. To find the time for the 13-mile race, multiply her 13-mile pace by the distance: 8 minutes/mile × 13 miles = 104 minutes. Options A (34), B (78), C (92), and D (101) all reflect incorrect calculations or misunderstandings of her pacing difference and distance, leading to values that do not align with the established pace of 8 minutes per mile.