This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
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Here are the solutions to the problems: 38. The figure above, not drawn to scale, consists of a triangle resting on a square of side 5 cm. The height of the triangle is 4 cm. What is the TOTAL area of the figure? Step 1: Calculate the area of the square. The side of the square is 5 cm. Area of square = side × side = 5 cm × 5 cm = 25 cm^2 Step 2: Calculate the area of the triangle. The base of the triangle is the same as the side of the square, which is 5 cm. The height of the triangle is 4 cm. Area of triangle = (1)/(2) × base × height = (1)/(2) × 5 cm × 4 cm = 10 cm^2 Step 3: Calculate the total area of the figure. Total area = Area of square + Area of triangle = 25 cm^2 + 10 cm^2 = 35 cm^2 The correct option is (A). A) 35 cm^2 39. The diagram, not drawn to scale, shows a cylinder of radius 3 cm and height of 8 cm. The volume is Step 1: Identify the formula for the volume of a cylinder. V = r^2 h where r is the radius and h is the height. Step 2: Substitute the given values into the formula. Given r = 3 cm and h = 8 cm. V = (3 cm)^2 (8 cm) Step 3: Calculate the volume. V = (9 cm^2) (8 cm) = 72 cm^3 The correct option is (C). C) 72 cm^3 40. On leaving Trinidad, a pilot watched time 23:00 hrs. He arrived at his destination, 03:00 hrs on the following day. How long did the flight take? Step 1: Calculate the time remaining on the first day. Departure time is 23:00 hrs. The day ends at 24:00 hrs (or 00:00 hrs of the next day). Time remaining on Day 1 = 24:00 hrs - 23:00 hrs = 1 hour Step 2: Add the time spent on the second day. Arrival time is 03:00 hrs on the following day. Total flight time = 1 hour + 3 hours = 4 hours The correct option is (A). A) 4 hrs 41. The mode of the number is The given numbers are 4, 7, 10, 18, 27. The mode is the value that appears most frequently in a data set. In this set, all numbers appear only once. Therefore, there is no mode. However, since this is a multiple-choice question and "no mode" is not an option, it is possible the question intended to ask for the median. Step 1: Arrange the numbers in ascending order. 4, 7, 10, 18, 27 Step 2: Identify the middle value (median). The middle value in this ordered set of 5 numbers is 10. Assuming the question implicitly asks for the median due to the options provided: The correct option is (A). A) 10 42. The bar chart shows the ages of children who took part in a survey. How many children took part in a survey? Step 1: Read the number of children for each age group from the bar chart. • Age 4: 3 children • Age 5: 5 children • Age 6: 4 children • Age 7: 2 children • Age 8: 1 child Step 2: Sum the number of children from all age groups. Total children = 3 + 5 + 4 + 2 + 1 = 15 The correct option is (B). B) 15 43. In a class of 20 students, 12 are girls. What is the probability that a student chosen at random is a boy? Step 1: Determine the total number of students. Total students = 20 Step 2: Determine the number of boys. Number of boys = Total students - Number of girls = 20 - 12 = 8 Step 3: Calculate the probability of choosing a boy. P(boy) = Number of boysTotal students = (8)/(20) Step 4: Simplify the fraction. P(boy) = (8 ÷ 4)/(20 ÷ 4) = (2)/(5) The correct option is (B). \