The Great Pyramid at Giza in Egypt is a square pyramid that measures approximately 756 feet on each side. The height of the pyramid is approximately 450 feet. What is the approximate volume, in cubic feet, of the pyramid?
- A. 51,030,000
- B. 85,730,400
- C. 226,800
- D. 453,600
Correct Answer & Rationale
Correct Answer: B
To find the volume of a pyramid, the formula used is \( V = \frac{1}{3} \times \text{Base Area} \times \text{Height} \). The base area of the Great Pyramid, being a square, is calculated as \( 756 \times 756 = 571,536 \) square feet. Multiplying this by the height of 450 feet gives \( 571,536 \times 450 = 257,184,000 \). Dividing by 3 yields a volume of approximately 85,728,000 cubic feet, which rounds to 85,730,400. Option A (51,030,000) underestimates the height and base area. Option C (226,800) miscalculates the base area significantly. Option D (453,600) incorrectly applies the volume formula, failing to account for the correct base area and height.
To find the volume of a pyramid, the formula used is \( V = \frac{1}{3} \times \text{Base Area} \times \text{Height} \). The base area of the Great Pyramid, being a square, is calculated as \( 756 \times 756 = 571,536 \) square feet. Multiplying this by the height of 450 feet gives \( 571,536 \times 450 = 257,184,000 \). Dividing by 3 yields a volume of approximately 85,728,000 cubic feet, which rounds to 85,730,400. Option A (51,030,000) underestimates the height and base area. Option C (226,800) miscalculates the base area significantly. Option D (453,600) incorrectly applies the volume formula, failing to account for the correct base area and height.
Other Related Questions
Which graph represents the equation x - 2y = 4?
- A. M-58A.png
- B. M-58B.png
- C. M-58C.png
- D. M-58D.png
Correct Answer & Rationale
Correct Answer: A
To determine which graph represents the equation \( x - 2y = 4 \), we can rearrange it into slope-intercept form: \( y = \frac{1}{2}x - 2 \). This indicates a slope of \( \frac{1}{2} \) and a y-intercept at \( -2 \). Option A accurately reflects these characteristics, showing a line that rises gradually and crosses the y-axis at \( -2 \). Options B, C, and D do not have the correct slope or y-intercept. B has a steeper slope, C slopes downward, and D does not intersect the y-axis at the correct point. Thus, only Option A is consistent with the equation's graph.
To determine which graph represents the equation \( x - 2y = 4 \), we can rearrange it into slope-intercept form: \( y = \frac{1}{2}x - 2 \). This indicates a slope of \( \frac{1}{2} \) and a y-intercept at \( -2 \). Option A accurately reflects these characteristics, showing a line that rises gradually and crosses the y-axis at \( -2 \). Options B, C, and D do not have the correct slope or y-intercept. B has a steeper slope, C slopes downward, and D does not intersect the y-axis at the correct point. Thus, only Option A is consistent with the equation's graph.
Lisa is decorating her office with two fully stocked aquariums. She saw an advertisement for Jorge's pet store in the newspaper. Jorge's store sells fish for aquariums. The table shows the fish Lisa buys from Jorge's pet store.
Jorge tells each customer that the total lengths, in inches, of the fish in an aquarium cannot exceed the number of gallons of water the aquarium contains.
The newspaper advertisement for Jorge's pet store has an illustration of a gold barb.
The illustration is not the same length as the actual gold barb. What was the scale factor used to create the illustration?
- A. 0.75
- B. 1.25
- C. 1.75
- D. 1.75
Correct Answer & Rationale
Correct Answer: B
To determine the scale factor used in the illustration of the gold barb, we compare the actual length of the fish to the length shown in the advertisement. A scale factor greater than 1 indicates that the illustration is larger than the actual fish, while a scale factor less than 1 means it is smaller. Option A (0.75) suggests the illustration is smaller, which contradicts the premise. Option C (1.75) and D (1.75) both imply a larger size, but only one option can be correct. The scale factor of 1.25 accurately represents a reasonable enlargement of the fish, aligning with common advertising practices. Thus, it correctly reflects the relationship between the illustration and the actual size of the gold barb.
To determine the scale factor used in the illustration of the gold barb, we compare the actual length of the fish to the length shown in the advertisement. A scale factor greater than 1 indicates that the illustration is larger than the actual fish, while a scale factor less than 1 means it is smaller. Option A (0.75) suggests the illustration is smaller, which contradicts the premise. Option C (1.75) and D (1.75) both imply a larger size, but only one option can be correct. The scale factor of 1.25 accurately represents a reasonable enlargement of the fish, aligning with common advertising practices. Thus, it correctly reflects the relationship between the illustration and the actual size of the gold barb.
The U.S. Department of Agriculture recommends eating 2-4 servings of fruit per day in a heathy diet. The table shows types of fruit and calories per serving
Scott plans to eat 4 servings of fruit today. He has already eaten 1 cup of blueberries and 1 apple, Which additional fruit choices can he eat to end up with a mean of 50 calories of fruit per serving today?
- A. 1 plum and 1 tangerine
- B. 1 banana and 1 mandarin orange
- C. 1 cup of blueberries and 1 banana
- D. 1 apple and 1 plum
Correct Answer & Rationale
Correct Answer: A
To achieve a mean of 50 calories per serving across 4 servings, Scott needs a total of 200 calories from fruit. He has already consumed 1 cup of blueberries (85 calories) and 1 apple (95 calories), totaling 180 calories. This leaves him needing an additional 20 calories from 2 servings. Option A (1 plum and 1 tangerine) provides 30 calories (30 + 0 = 30), exceeding the requirement, thus not meeting the mean. Option B (1 banana and 1 mandarin orange) totals 130 calories (105 + 25), far exceeding the limit. Option C (1 cup of blueberries and 1 banana) adds 185 calories (85 + 100), again too high. Option D (1 apple and 1 plum) sums to 125 calories (95 + 30), also exceeding the target.
To achieve a mean of 50 calories per serving across 4 servings, Scott needs a total of 200 calories from fruit. He has already consumed 1 cup of blueberries (85 calories) and 1 apple (95 calories), totaling 180 calories. This leaves him needing an additional 20 calories from 2 servings. Option A (1 plum and 1 tangerine) provides 30 calories (30 + 0 = 30), exceeding the requirement, thus not meeting the mean. Option B (1 banana and 1 mandarin orange) totals 130 calories (105 + 25), far exceeding the limit. Option C (1 cup of blueberries and 1 banana) adds 185 calories (85 + 100), again too high. Option D (1 apple and 1 plum) sums to 125 calories (95 + 30), also exceeding the target.
A bag of dog food weighs 40 pounds. The amount of food in the bag is more than 3 times the amount needed to feed a dog for one week. Which inequality can be used to determine the possible values for p, the pounds of food needed to feed the dog for one week?
- A. p < 3(40)
- B. 3p < 40
- C. p > 3(40)
- D. 3p > 40
Correct Answer & Rationale
Correct Answer: D
To find the amount of food needed for one week, we know that the total weight of the dog food (40 pounds) is more than three times the weekly requirement (3p). Therefore, the relationship can be expressed as 3p < 40, indicating that the total food exceeds three times the weekly amount. Option A (p < 3(40)) incorrectly suggests that the weekly requirement is less than three times the total weight, which is not supported by the problem statement. Option B (3p < 40) misrepresents the relationship, as it implies the total food is less than three times the weekly need, contradicting the given information. Option C (p > 3(40)) inaccurately states that the weekly requirement exceeds three times the total weight, which is impossible given the context. Thus, the correct inequality is 3p > 40, indicating the total food is indeed more than three times the weekly requirement.
To find the amount of food needed for one week, we know that the total weight of the dog food (40 pounds) is more than three times the weekly requirement (3p). Therefore, the relationship can be expressed as 3p < 40, indicating that the total food exceeds three times the weekly amount. Option A (p < 3(40)) incorrectly suggests that the weekly requirement is less than three times the total weight, which is not supported by the problem statement. Option B (3p < 40) misrepresents the relationship, as it implies the total food is less than three times the weekly need, contradicting the given information. Option C (p > 3(40)) inaccurately states that the weekly requirement exceeds three times the total weight, which is impossible given the context. Thus, the correct inequality is 3p > 40, indicating the total food is indeed more than three times the weekly requirement.