Solved on Mar 10, 2024

Find the area of a pizza slice with a central angle of $23^{\circ}$ from an 18-inch diameter pizza. The area is approximately $\square$ square inches (rounded to two decimal places).

STEP 1

Assumptions
1. The diameter of the pizza is 18 inches.
2. The pizza is circular in shape.
3. A piece of pizza is cut with a central angle of $23^{\circ}$ .
4. The area of the pizza slice can be found by calculating the area of the sector of the circle with the given central angle.
5. The formula to calculate the area of a sector of a circle is given by $\frac{\theta}{360} \times \pi r^2$ , where $\theta$ is the central angle in degrees and $r$ is the radius of the circle.

STEP 2

First, we need to find the radius of the pizza. Since the diameter is given, the radius is half of the diameter.
$Radius = \frac{Diameter}{2}$

STEP 3

Now, plug in the given diameter to calculate the radius.
$Radius = \frac{18\, inches}{2}$

STEP 4

Calculate the radius.
$Radius = 9\, inches$

STEP 5

Next, we will use the formula for the area of a sector of a circle to find the area of the pizza slice.
$Area\, of\, sector = \frac{\theta}{360} \times \pi r^2$

STEP 6

Plug in the values for the central angle and the radius into the formula.
$Area\, of\, sector = \frac{23^{\circ}}{360} \times \pi \times (9\, inches)^2$

STEP 7

Calculate the area of the sector (pizza slice).
$Area\, of\, sector = \frac{23}{360} \times \pi \times 81\, inches^2$

STEP 8

Perform the multiplication to find the area.
$Area\, of\, sector = \frac{23}{360} \times \pi \times 81\, inches^2 \approx 51.84\, inches^2$

STEP 9

Round the area to two decimal places as needed.
$Area\, of\, sector \approx 51.84\, inches^2$
The area of the piece of pizza is approximately $51.84$ square inches.

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Find the area of a pizza slice with a central angle of $23^{\circ}$ from an 18-inch diameter pizza. The area is approximately $\square$ square inches (rounded to two decimal places).

STEP 1

STEP 2

First, we need to find the radius of the pizza. Since the diameter is given, the radius is half of the diameter.
$Radius = \frac{Diameter}{2}$

STEP 3

Now, plug in the given diameter to calculate the radius.
$Radius = \frac{18\, inches}{2}$

STEP 4

Calculate the radius.
$Radius = 9\, inches$

STEP 5

Next, we will use the formula for the area of a sector of a circle to find the area of the pizza slice.
$Area\, of\, sector = \frac{\theta}{360} \times \pi r^2$

STEP 6

Plug in the values for the central angle and the radius into the formula.
$Area\, of\, sector = \frac{23^{\circ}}{360} \times \pi \times (9\, inches)^2$

STEP 7

Calculate the area of the sector (pizza slice).
$Area\, of\, sector = \frac{23}{360} \times \pi \times 81\, inches^2$

STEP 8

Perform the multiplication to find the area.
$Area\, of\, sector = \frac{23}{360} \times \pi \times 81\, inches^2 \approx 51.84\, inches^2$

STEP 9

Round the area to two decimal places as needed.
$Area\, of\, sector \approx 51.84\, inches^2$
The area of the piece of pizza is approximately $51.84$ square inches.

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Find the area of a pizza slice with a central angle of 23∘23^{\circ}23∘ from an 18-inch diameter pizza. The area is approximately □\square□ square inches (rounded to two decimal places).

STEP 1

STEP 2

First, we need to find the radius of the pizza. Since the diameter is given, the radius is half of the diameter.Radius=Diameter2Radius = \frac{Diameter}{2}Radius=2Diameter​

STEP 3

Now, plug in the given diameter to calculate the radius.Radius=18 inches2Radius = \frac{18\, inches}{2}Radius=218inches​

STEP 4

Calculate the radius.Radius=9 inchesRadius = 9\, inchesRadius=9inches

STEP 5

Next, we will use the formula for the area of a sector of a circle to find the area of the pizza slice.Area of sector=θ360×πr2Area\, of\, sector = \frac{\theta}{360} \times \pi r^2Areaofsector=360θ​×πr2

STEP 6

Plug in the values for the central angle and the radius into the formula.Area of sector=23∘360×π×(9 inches)2Area\, of\, sector = \frac{23^{\circ}}{360} \times \pi \times (9\, inches)^2Areaofsector=36023∘​×π×(9inches)2

STEP 7

Calculate the area of the sector (pizza slice).Area of sector=23360×π×81 inches2Area\, of\, sector = \frac{23}{360} \times \pi \times 81\, inches^2Areaofsector=36023​×π×81inches2

STEP 8

Perform the multiplication to find the area.Area of sector=23360×π×81 inches2≈51.84 inches2Area\, of\, sector = \frac{23}{360} \times \pi \times 81\, inches^2 \approx 51.84\, inches^2Areaofsector=36023​×π×81inches2≈51.84inches2

STEP 9

Round the area to two decimal places as needed.Area of sector≈51.84 inches2Area\, of\, sector \approx 51.84\, inches^2Areaofsector≈51.84inches2The area of the piece of pizza is approximately 51.8451.8451.84 square inches.

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Find the area of a pizza slice with a central angle of $23^{\circ}$ from an 18-inch diameter pizza. The area is approximately $\square$ square inches (rounded to two decimal places).

First, we need to find the radius of the pizza. Since the diameter is given, the radius is half of the diameter.
$Radius = \frac{Diameter}{2}$

Now, plug in the given diameter to calculate the radius.
$Radius = \frac{18\, inches}{2}$

Calculate the radius.
$Radius = 9\, inches$

Next, we will use the formula for the area of a sector of a circle to find the area of the pizza slice.
$Area\, of\, sector = \frac{\theta}{360} \times \pi r^2$

Plug in the values for the central angle and the radius into the formula.
$Area\, of\, sector = \frac{23^{\circ}}{360} \times \pi \times (9\, inches)^2$

Calculate the area of the sector (pizza slice).
$Area\, of\, sector = \frac{23}{360} \times \pi \times 81\, inches^2$

Perform the multiplication to find the area.
$Area\, of\, sector = \frac{23}{360} \times \pi \times 81\, inches^2 \approx 51.84\, inches^2$

Round the area to two decimal places as needed.
$Area\, of\, sector \approx 51.84\, inches^2$
The area of the piece of pizza is approximately $51.84$ square inches.