Arc Length and Sector Area Quiz

Answer explanation

To find the arc length, use the formula: Arc Length = (Central Angle/360) * (2 * π * Radius). Here, it is (60/360) * (2 * π * 7) = 7.33 cm. Thus, the correct answer is 7.33 cm.

Tags

VA.MATH.9-12.G.PC.3.d

Answer explanation

The length of an arc is given by the formula \( L = \frac{\theta}{360} \times 2\pi r \). Here, \( \theta = 90^\circ \) and \( r = 10 \) cm. Thus, \( L = \frac{90}{360} \times 2\pi \times 10 = 5\pi \) cm.

Tags

VA.MATH.9-12.G.PC.3.d

Answer explanation

The area of a sector is given by the formula \( A = \frac{\theta}{360} \times \pi r^2 \). Here, \( \theta = 120^\circ \) and \( r = 12 \) cm. Thus, \( A = \frac{120}{360} \times \pi (12)^2 = 48\pi \) cm².

Tags

VA.MATH.9-12.G.PC.3.e

Answer explanation

The area of a sector is given by the formula A = (θ/360) * πr². Here, θ = 45° and r = 8 cm. Thus, A = (45/360) * π * (8)² = (1/8) * π * 64 = 8π/2 = 4π cm². Therefore, the correct answer is 4π cm².

Tags

VA.MATH.9-12.G.PC.3.e

Answer explanation

The formula for the length of an arc is L = r * θ, where L is the arc length, r is the radius, and θ is the central angle in radians. Here, θ = 180° = π radians. Thus, 6π = r * π, leading to r = 6 cm.

Tags

VA.MATH.9-12.G.PC.3.f

Answer explanation

The area of a sector is given by the formula A = (θ/360) * πr². Here, A = 25π and θ = 90°. Plugging in the values: 25π = (90/360) * πr². Simplifying gives r² = 100, so r = 10 cm.

Tags

VA.MATH.9-12.G.PC.3.f

Answer explanation

The radius is 10 cm (half of the diameter). The arc length is given by \( L = \frac{\theta}{360} \times 2\pi r \). Substituting \( \theta = 72 \) and \( r = 10 \), we get \( L = \frac{72}{360} \times 20\pi = 4\pi \) cm.

Tags

VA.MATH.9-12.G.PC.3.d

Answer explanation

The area of a sector is given by the formula A = (θ/360) * πr². Here, θ = 60° and r = 14 cm. Thus, A = (60/360) * π * (14)² = (1/6) * π * 196 = 28π cm². Therefore, the correct answer is 28π cm².

Tags

VA.MATH.9-12.G.PC.3.e

Answer explanation

The area of a sector is given by the formula A = (θ/360) * πr². Plugging in A = 18π and r = 9, we get 18π = (θ/360) * π(9)². Simplifying, θ = 120°. Thus, the central angle is 120°.

Tags

VA.MATH.9-12.G.PC.3.f

Answer explanation

The formula for the length of an arc is L = (θ/360) * 2πr. Here, L = 5π cm and r = 5 cm. Plugging in the values: 5π = (θ/360) * 2π(5). Simplifying gives θ = 180°. Thus, the central angle is 180°.

Tags

VA.MATH.9-12.G.PC.3.f