Let's solve each part step by step:
a. Angle 49°
This is already in number form: 49°
b. Angle 270°
This is already in number form: 270°
c. Circle with a radius of 3 cm
The area \( A \) of a circle is calculated using the formula: \[ A = \pi r^2 \] Substituting the radius \( r = 3 \) cm: \[ A \approx 3.14 \times (3)^2 \approx 3.14 \times 9 \approx 28.26 , \text{cm}^2 \]
Answer: 28.26 cm²
d. Line AB // CD 4 cm apart and line EF # AB + CD
If line AB is parallel to line CD and they are 4 cm apart, we haven't been given sufficient information about EF. However, if the intention is to say that EF is also a line that runs between AB and CD or parallels them, no direct calculation can be made without additional information. Thus, we can't calculate a number here without assumptions.
Assuming a simpler interpretation, the distance between the lines is 4 cm.
Answer: 4 cm (for spacing between parallels)
e. Calculate the area of a 12 cm by 7 cm rectangle
The area \( A \) of a rectangle is calculated using the formula: \[ A = \text{length} \times \text{width} \] Substituting \( 12 , \text{cm} \) and \( 7 , \text{cm} \): \[ A = 12 \times 7 = 84 , \text{cm}^2 \]
Answer: 84 cm²
f. Calculate the volume of a cube with side lengths of 4 m
The volume \( V \) of a cube is calculated using the formula: \[ V = \text{side}^3 \] Substituting the side length \( 4 , \text{m} \): \[ V = 4^3 = 64 , \text{m}^3 \]
Answer: 64 m³
g. Calculate the area of the shaded region if the triangle has a base of 3 m and a height of 2 m
The area \( A \) of a triangle is calculated using the formula: \[ A = \frac{1}{2} \times \text{base} \times \text{height} \] Substituting the base and height: \[ A = \frac{1}{2} \times 3 \times 2 = \frac{6}{2} = 3 , \text{m}^2 \]
Answer: 3 m²
Summary of Answers
- a. 49°
- b. 270°
- c. 28.26 cm²
- d. 4 cm
- e. 84 cm²
- f. 64 m³
- g. 3 m²