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PtichkaEL [24]
10 months ago
11

Find the length of the arc and express your answer as a fraction times pie

Mathematics
1 answer:
Elina [12.6K]10 months ago
4 0

Solution:

Given a circle of center, A with radius, r (AB) = 6 units

Where, the area, A, of the shaded sector, ABC, is 9π

To find the length of the arc, firstly we will find the measure of the angle subtended by the sector.

To find the area, A, of a sector, the formula is

\begin{gathered} A=\frac{\theta}{360\degree}\times\pi r^2 \\ Where\text{ r}=AB=6\text{ units} \\ A=9\pi\text{ square units} \end{gathered}

Substitute the values of the variables into the formula above to find the angle, θ, subtended by the sector.

\begin{gathered} 9\pi=\frac{\theta}{360\degree}\times\pi\times6^2 \\ Crossmultiply \\ 9\pi\times360=36\pi\times\theta \\ 3240\pi=36\pi\theta \\ Divide\text{ both sides by 36}\pi \\ \frac{3240\pi}{36\pi}=\frac{36\pi\theta}{36\pi} \\ 90\degree=\theta \\ \theta=90\degree \end{gathered}

To find the length of the arc, s, the formula is

\begin{gathered} s=\frac{\theta}{360\degree}\times2\pi r \\ Where \\ \theta=90\degree \\ r=6\text{ units} \end{gathered}

Substitute the variables into the formula to find the length of an arc, s above

\begin{gathered} s=\frac{\theta}{360}\times2\pi r \\ s=\frac{90\degree}{360\degree}\times2\times\pi\times6 \\ s=\frac{12\pi}{4}=3\pi\text{ units} \\ s=3\pi\text{ units} \end{gathered}

Hence, the length of the arc, s, is 3π units.

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Serjik [45]

Surface area of the solid = 7.1781 in²

Volume of the solid = 0.804 in³

Explanation:

Surface area of the solid = surface area of the square prism - 2(base of the cylinder) + lateral surface of cylinder

surface area of a square prism = 2(lw + lh + wh)

l = length = 1 in

w = length = 1 in

h = height = 1 in

\begin{gathered} \text{Surface area = 2(1}\times1\text{ + 1}\times1\text{ + 1}\times1) \\ \text{Surface area = 2(1 + 1 + 1) = 2(3)} \\ \text{Surface area = 6 in }^2 \end{gathered}

using the value π as it is on the calculator

Base area of a cylinder = πr²

2(Base area of cylinder) = 2πr² = 2π(0.25)² = 0.3927

Lateral surface area = 2πrh = 2π(0.25)(1) = 1.5708

Surface area of the solid = 6 - 0.3927 + 1.5708

Surface area of the solid = 7.178 in²

Volume of the solid = Volume of the square prism - volume of the cylinder

Volume of square prism = length × width × height

length = 1 in, width = 1 in, height = 1 in

Volume of the solid = 1 in × 1 in × 1 in = 1 in³

Volume of a cylinder = πr²h

Volume of the cylinder = π × 0.25 × 0.25 × 1 = 0.196

Volume of the solid = 1 - 0.196

Volume of the solid = 0.804 in³

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1 year ago
Are the two shapes are congruent?​
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Answer:

nah

Step-by-step explanation:

the distance between H and G is longer than the distance between C and D making it not congruent

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What is the domain of the function y=\sqrt{x}
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Step-by-step explanation:

Square roots cannot hold negative x values as it will create an imaginary number.

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Give the slope-intercept form of the equation of the line that is perpendicular to –7x – 8y = 12 and contains P(–3, 1)
snow_lady [41]

Answer:

(-7/8)

Step-by-step explanation:

the line is  -7x -8y =12

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