Question

A slice of pizza is shown below. the slice is a sector of a circular pizza. calculate the area of the slice of pizza. give your answer in cm² to 1 d.p. 32° 14 cm

Answer 1

The area of the pizza slice, which is a sector of a circle with a 32° angle and 14 cm radius, is approximately 54.7 cm² when calculated using the sector area formula and rounded to two significant figures.

Step-by-step explanation:

The student wants to calculate the area of a pizza slice which is a sector of a circle with a given radius and angle. To find the area of the sector, we need to know the formula for the area of a circle, which is A = πr². However, since a sector is only a portion of a circle, we adjust this formula by multiplying with the fraction of the circle that the sector represents.

The formula for the sector's area is:

Area of Sector = (θ/360) × πr²

where θ is the angle in degrees and r is the radius in centimeters. In this case, the given angle is 32° and the radius is 14 cm. Substituting these values into the formula:

Area of Sector = (32°/360°) × π(14 cm)²

Using a calculator with the value of π as 3.1415927 (or rounded to 3.14 for simplicity), we calculate the area. Because the radius (14 cm) has two significant figures, we should give the final answer to two significant figures or one decimal place if necessary.

Calculation steps:

1. 
   
3. Multiply the radius by itself: 14 cm x 14 cm = 196 cm².
4. 
   
6. Multiply this result by π: 196 cm² × 3.14 ≈ 615.44 cm².
7. 
   
9. Adjust for the sector by multiplying by the fraction (θ/360): 615.44 cm² × (32°/360°) ≈ 54.6827 cm².
10. 
    
12. Round to two significant figures: The area is approximately 54.7 cm².

Answer 2

1) The area of the pizza slice is approximately 33.4 cm².

2) This is calculated using the formula for the area of a sector:
`\( \text{Area} = (\theta)/(360) * \pi r^2 \),` where
`\( \theta \)` is the central angle in degrees,
`\( \pi \)` is a mathematical constant (approximately 3.14159), and r is the radius.

Step-by-step explanation:

1) To calculate the area of the pizza slice, we use the formula for the area of a sector of a circle. The given central angle is 32°, and the radius is 14 cm. Plugging these values into the formula, we get
`\( \text{Area} = (32)/(360) * 3.14159 * (14)^2 \)`.

2) The calculation yields an area of approximately 33.4 cm², rounded to one decimal place. This represents the portion of the circular pizza defined by the central angle.