If the arc length of the fan is 20cm and the radius is 5cm, then its area is______ cm2．

If the arc length of the fan is 20cm and the radius is 5cm, then its area is______ cm2．

S=1
2LR=1
2×20×5=50cm2．

The radii of the upper and lower bottom surfaces of the cone are 10cm and 20cm respectively, and the center angle of the fan ring in the side expansion diagram is 180 ° so what are the side area, surface area and volume of the cone? (retain π in the result)

If the bus length of the cone is l, then 20 − 10
l×360°=180°⇒l=20，
The lateral product s of the cone s side = π (10 + 20) × 20 = 600 π (cm2);
The surface area of the cone s = π × 102 + π × 202 + 600 π = 1100 π (cm2);
The height of the cone is
202−102=10
3，
The volume of the cone is v = 1
3π（100+400+10×20）×10
3=7000
Three
3π（cm3）．

If the circumference of the sector is 16 cm and the center angle of the circle is 2 radians, then the area of the sector is______ .

Let the sector radius r, the area s and the center angle α, then α = 2 and the arc length α R,
Then the circumference is 16 = 2R + α r = 2R + 2R = 4R, νr = 4,
The area of the sector is: S = 1
2α r2=1
2 × 2 × 16 = 16 (cm2), so the answer is 16 cm2

If the radius of a sector is 5 cm and the arc length is 6.28 cm, then the area of the sector is -------- cm 2

thirty-one point four

The radius of the sector is 5cm and the area is 15.7cm2. What is the circumference of the sector

Center angle = 15.7 × (5 × 5 × 3.14) × 360 = 72 degrees
Circumference = 5 × 2 × 3.14 × 72 / 360 + 5 × 2 = 16.28 cm

As shown in the figure, sector AOB, the center angle of the circle AOB is equal to 60 ° and the radius is 2. There is a moving point P on the arc ab. the straight line parallel to ob and OA intersect at point C through P, and let ∠ AOP = θ, calculate the maximum area of △ POC and the value of θ at this time

Do PD ⊥ Ao through point P
PD is the height of △ POC. Let it be d
Then de = Tan ∠ AOP * d = √ 3D
DO=tanθ*d
EO=DO-ED=√3d-tanθ*d=d(√3-tanθ).
d=PO*sinθ=2sinθ
So s △ AOP = 1 / 2 * 2 * sin θ * 2 * sin θ (√ 3-tan θ)
=[(√3-tanθ)(2sinθ)^2]/2=2sinθ^2*(√3-tanθ)
According to the basic inequality
When d = De, the triangle area is the largest,
Therefore, when θ = 45 degrees, the area is the largest, s = √ 3-1

In circle O, if the angle of arc AB to the center of circle is 60 degrees, then the length of arc AB is the circumference of circle?

6 × 60 = 360, 1 / 6 perimeter

Known: the center angle of the sector is 60 degrees, and its arc length AB is 3 π cm. Calculate the chord length of ab

Arc length = radius * center angle,
So radius = 3 π / (π / 3) = 9,
So chord length = radius = 9cm
According to the formula, the chord length of sphere AB = radius = 9cm. (equilateral triangle)

Given the square of arc AB, the center angle of arc AB is 60 ° and the radius of circle AB is found Given that the radius of an arc is 10 cm and the length of an arc is 12 cm, calculate the degree of the arc

Given that the square of arc AB is C, and the angle a of the center of the circle to which arc AB is directed is 60 °, find the radius r? Of the circle where arc AB is located?
A = 60 ° = 60 ° * pi / 180 ° = pi / 3 radian
R=C^0.5/A=C^0.5/(PI/3)=(3*C^0.5)/PI
Given that the radius is r = 10cm and the length of an arc in the circle is C = 12cm, find the degree of this arc a?
A = C / r = 12 / 10 = 1.2 radian = 1.2 * 180 / pi = 68.755 degrees

For a circle with a radius of 6cm, the arc length of a circle center angle is 6.28cm. How many degrees is the central angle of the circle?

180×6.28
14 × 6 = 60 (degree),
A: the center angle of the circle is 60 degrees