A circle with area 36 pi has a sector with a central angle of 48^(@). What is the area of the sector? Choose 1 answer: (A) (5)/(24)pi B (1)/(270)pi (C) 270 pi (D) (24)/(5)pi

Identify Formula: Identify the formula to calculate the area of a sector of a circle. The area of a sector is given by the formula: (central angle / 360) * π * r^2, where r is the radius of the circle.Find Radius: Find the radius of the circle using the area of the circle. The area of the circle is given as 36π, and the formula for the area of a circle is π * r^2. We can set up the equation 36π = π * r^2 and solve for r. 36π = π * r^2 r^2 = 36 r = √36 r = 6Calculate Sector Area: Calculate the area of the sector using the radius and the central angle. Now that we know the radius (r = 6) and the central angle (48 degrees), we can use the sector area formula: (sector area) = (48 / 360) * π * (6)^2 (sector area) = (48 / 360) * π * 36 (sector area) = (4 / 30) * π * 36 (sector area) = (2 / 15) * π * 36 (sector area) = (2 * 36) / 15 * π (sector area) = 72 / 15 * π (sector area) = 4.8 * πSimplify Area: Simplify the sector area to match one of the given answer choices. (sector area) = 4.8 * π This does not match any of the answer choices exactly, but we can convert it to a fraction: (sector area) = (24 / 5) * π This matches answer choice (D).

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A circle with area
36 pi has a sector with a central angle of
48^(@). What is the area of the sector?
Choose 1 answer:
(A)
(5)/(24)pi
B
(1)/(270)pi
(C)
270 pi
(D)
(24)/(5)pi

Acircle with area $36 \pi$ has a sector with a central angle of $48^{\circ}$ . What is the area of the sector? $\newline$ Choose $1$ answer: $\newline$ (A) $\frac{5}{24} \pi$ $\newline$ (B) $\frac{1}{270} \pi$ $\newline$ (C) $270 \pi$ $\newline$ (D) $\frac{24}{5} \pi$ $\newline$

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Math Problems

Grade 6

Area of quadrilaterals and triangles: word problems

Full solution

Q. Acircle with area

36 \pi

has a sector with a central angle of

48^{\circ}

. What is the area of the sector?

\newline

Choose

1

answer:

\newline

(A)

\frac{5}{24} \pi

\newline

(B)

\frac{1}{270} \pi

\newline

(C)

270 \pi

\newline

(D)

\frac{24}{5} \pi

\newline

Identify Formula: Identify the formula to calculate the area of a sector of a circle. $\newline$ The area of a sector is given by the formula: $(\frac{\text{central angle}}{360}) \times \pi \times r^2$ , where $r$ is the radius of the circle.
Find Radius: Find the radius of the circle using the area of the circle. $\newline$ The area of the circle is given as $36\pi$ , and the formula for the area of a circle is $\pi * r^2$ . We can set up the equation $36\pi = \pi * r^2$ and solve for $r$ . $\newline$ $36\pi = \pi * r^2$ $\newline$ $r^2 = 36$ $\newline$ $r = \sqrt{36}$ $\newline$ $r = 6$
Calculate Sector Area: Calculate the area of the sector using the radius and the central angle. $\newline$ Now that we know the radius $r = 6$ and the central angle $48$ degrees, we can use the sector area formula: $\newline$ $\text{(sector area)} = \frac{48}{360} \times \pi \times (6)^2$ $\newline$ $\text{(sector area)} = \frac{48}{360} \times \pi \times 36$ $\newline$ $\text{(sector area)} = \frac{4}{30} \times \pi \times 36$ $\newline$ $\text{(sector area)} = \frac{2}{15} \times \pi \times 36$ $\newline$ $\text{(sector area)} = \frac{2 \times 36}{15} \times \pi$ $\newline$ $\text{(sector area)} = \frac{72}{15} \times \pi$ $\newline$ $\text{(sector area)} = 4.8 \times \pi$
Simplify Area: Simplify the sector area to match one of the given answer choices. $\newline$ $(\text{sector area}) = 4.8 \times \pi$ $\newline$ This does not match any of the answer choices exactly, but we can convert it to a fraction: $\newline$ $(\text{sector area}) = \left(\frac{24}{5}\right) \times \pi$ $\newline$ This matches answer choice $(D)$ .