A figure 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? A cylinder has radius 3 cm and height 8 cm. What is its volu

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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 $5 \text{ cm}$.

$$\text{Area of square} = \text{side} \times \text{side} = 5 \text{ cm} \times 5 \text{ cm} = 25 \text{ cm}^2$$

Step 2: Calculate the area of the triangle.
The base of the triangle is the same as the side of the square, which is $5 \text{ cm}$. The height of the triangle is $4 \text{ cm}$.

$$\text{Area of triangle} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 5 \text{ cm} \times 4 \text{ cm} = 10 \text{ cm}^2$$

Step 3: Calculate the total area of the figure.

$$\text{Total area} = \text{Area of square} + \text{Area of triangle} = 25 \text{ cm}^2 + 10 \text{ cm}^2 = 35 \text{ cm}^2$$

The correct option is (A).

$$\boxed{\text{A) } 35 \text{ cm}^2}$$

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.

$$V = \pi r^2 h$$

where $r$ is the radius and $h$ is the height.

Step 2: Substitute the given values into the formula.
Given $r = 3 \text{ cm}$ and $h = 8 \text{ cm}$.

$$V = \pi (3 \text{ cm})^2 (8 \text{ cm})$$

Step 3: Calculate the volume.

$$V = \pi (9 \text{ cm}^2) (8 \text{ cm}) = 72\pi \text{ cm}^3$$

The correct option is (C).

$$\boxed{\text{C) } 72\pi \text{ cm}^3}$$

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).

$$\text{Time remaining on Day 1} = 24:00 \text{ hrs} - 23:00 \text{ hrs} = 1 \text{ hour}$$

Step 2: Add the time spent on the second day.
Arrival time is 03:00 hrs on the following day.

$$\text{Total flight time} = 1 \text{ hour} + 3 \text{ hours} = 4 \text{ hours}$$

The correct option is (A).

$$\boxed{\text{A) } 4 \text{ hrs}}$$

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).

$$\boxed{\text{A) } 10}$$

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.

$$\text{Total children} = 3 + 5 + 4 + 2 + 1 = 15$$

The correct option is (B).

$$\boxed{\text{B) } 15}$$

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.

$$\text{Total students} = 20$$

Step 2: Determine the number of boys.

$$\text{Number of boys} = \text{Total students} - \text{Number of girls} = 20 - 12 = 8$$

Step 3: Calculate the probability of choosing a boy.

$$P(\text{boy}) = \frac{\text{Number of boys}}{\text{Total students}} = \frac{8}{20}$$

Step 4: Simplify the fraction.

$$P(\text{boy}) = \frac{8 \div 4}{20 \div 4} = \frac{2}{5}$$

The correct option is (B).

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