Who can help me to deduce the formula of cone side area? Why is s = π RL?

Who can help me to deduce the formula of cone side area? Why is s = π RL?

Analysis before solution: ① the derivation of the side area of the cone needs to expand the cone; ② mathematically, the line from the top of the cone to any point on the circle of the cone bottom is called the generatrix of the cone; ③ the plane figure formed by cutting along any generatrix of the cone is a sector; ④ the radius of the sector after expansion is

Why multiply 1 / 2 in the derivation of the formula of the side area of a cone
Is the area formula of a cone. 3.14xlxr is not 1 / 2lr

Extending from fan
(1) Circle area s = π R & sup2;
(2) The area of sector with center angle of 1 ° is π R & sup2 / 360;
(3) The area of the sector with the center angle of n ° is n times that of the sector with the center angle of 1 °;
(4) The area of sector with center angle of n ° is n π R & sup2 / 360
L=(2πRα)/360°
S=(LR²απ)/360°=LR/2
α is the angle, (if α is radian, replace 360 ° with 2 π) l is the arc length and S is the area
2. Expand the side of a cone along its generatrix (we call the line between the apex of the cone and any point on the circumference of the bottom surface the generatrix of the cone, do you know that?) into a plane figure. The expanded figure is a sector (you can see this) http://wenwen.soso.com/z/q47962781.htm (after expansion, the radius of the sector is the generatrix of the cone, and the arc length of the sector is the circumference of the bottom of the cone)
We know that the formula of sector area is: S = 1 / 2lr, that is, the sector area is equal to half of the arc length multiplied by the radius. Take this graph for example, OA is the radius r, so the arc length of sector is equal to 2 π R, SA is the radius L, so the sector area s = 1 / 2.2 π R · L = π RL, that is, the side area of cone s = π RL

There is a ring washer, the circumference of the outer circle is 25.12 cm, the circumference of the inner circle is 15.7 cm, what is the width of the ring washer

(25.12-15.7)/3.14/2=1.5

If the circumference of the circle is reduced to 12, the area of the circle will be the same______ ．

The original circle perimeter = 2 π R, area = π R2, reduced circle perimeter = 2 π R × 12 = π R, reduced circle radius = π R △ 2 π = R2, reduced circle area = π (R2) 2, π (R2) 2 △ π R2, = 14; so the answer is: 14

The diameter of a circle is 3 / 4 of that of B circle, the perimeter of a circle is a fraction of that of B circle, and the area of a circle is a fraction of that of B circle

The diameter of circle a is 3 / 4 of circle B, the perimeter of circle a is 3 / 4 of circle B, and the area of circle a is 9 / 16 of circle B

The perimeter of a circle is 12.56 cm, the perimeter of B circle is 1 / 4 of a circle, what is the area of B circle

The perimeter of B is 12.56 × 1 / 4 = 3.14 cm
So the radius is 3.14-2-3.14 = 0.5cm
So the area of B is 3.14 × 0.5 × 0.25 = 0.785 square centimeter

The area ratio of circle a and circle B is 4:9. The perimeter of circle a is 25.12 decimeters. What are the perimeter and area of circle B

Method 1 (easy to understand, inconvenient to calculate) it is known that the perimeter of circle a is 25.12 decimeters. According to the perimeter = 2x3.14x radius, the radius of circle a is 4. According to the square of area = 3.14x radius, the area of circle a is 50.24. Because the area ratio is 4:9, the area of circle B is 113.04

The radius of the big circle is equal to the diameter of the small circle. What's the circumference of the small circle? What's the area of the small circle?
What's the formula

The perimeter formula L = 2 π R and the area formula s = π R * r. it can be seen that the perimeter of a small circle is 1 / 2 of that of a large circle, and the area of a small circle is 1 / 4 of that of a large circle

The diameter of the circle is 10 cm. Find the circumference of the circle

3.14×10=31.4㎝

The diameter of circle a is 8 cm, which is 25% of the diameter of circle B. the circumference of circle B is______ ．

Diameter of circle B: 8 △ 25 = 20 (CM), perimeter of circle B: 3.14 × 20 = 62.8 (CM); answer: perimeter of circle B is 62.8 cm. So the answer is: 62.8 cm