The sector with radius of 10 and center angle of 216 ° forms a cone. What is the volume of the cone?

The sector with radius of 10 and center angle of 216 ° forms a cone. What is the volume of the cone?

If the arc length of the center angle 216 ° is 216 × 3.14 × 10 × 2360 = 37.68, then the circumference of the bottom surface of the cone is 37.68, then the radius of the bottom surface of the cone is 37.68 △ 3.14 △ 2 = 6; because the length of the generatrix is 10, so if the height of the cylinder is h, then h2 = 102-62 = 100-36 = 64, because 8 × 8 = 64, then H = 8

The degree of the central angle of a fan-shaped circle is 120. What is the ratio of the side surface to the bottom surface of a cone if it is used as the side surface of the cone

Square of PI x radius X120 / 360: square of PI x [(2x PI x radius X120 / 360) / 2x PI]
=3：1

If the radius of a sector is reduced to one-third of the original, and the central angle of the circle is expanded to nine times of the original, the area of the sector will be reduced_________

The radius and the angle of the center of the circle are regarded as 1
Now the radius is 1 / 3 and the center angle is 9
The original area π × 1 × 1 = π
Now π × 1 / 3 × 1 / 3 × 1 / 9 = π
So the area doesn't change

Given that the bottom radius of the cone is 5cm and the side area is 65 π cm2, let the angle between the generatrix and the height of the cone be θ, as shown in the figure, then the value of sin θ is ()
A. 512B. 513C. 1013D. 1213

According to the radius of the bottom of the cone is 5cm, the perimeter of the bottom is 10 π. According to the area formula of the sector s = 12L · R, then 65 π = 12.10 π· R, ∧ r = 13, so sin θ = 513. So B

The relationship between the cone and the fan
The fan-shaped encirclement of the city
The relationship between the enclosed cone and the sector

The circumference of the cone is the arc length of the sector, the side area of the cone is the area of the sector, and the generatrix of the cone is the radius of the sector

Cut off a sector iron sheet from a circular iron sheet with a radius of 50cm, and make a conical chimney cap with a bottom diameter of 80cm and a bus length of 50cm (as shown in the figure), then the degree of the center angle of the cut sector is______ ．

80 π = n π × 50180, the solution is n = 288 ° which is the remaining degree, then the cut degree is 360 ° - 288 ° = 72 °. So the answer is 72 °

The height of a cone is 10cm, the diameter of its bottom is 6cm, what is the generatrix? What is the formula?

Expand the side of a cone to get a sector whose radius is equal to the length of the generatrix of the cone;
Through the stereogram, you can see a right triangle composed of the height of the cone, the radius of the bottom, and the generatrix. The generatrix is a hypotenuse;
From Pythagorean theorem, it is concluded that: & nbsp;
Square of height + square of bottom radius = square of generatrix & nbsp;
So bus = root (10 square + 3 square) = root 109

As shown in the figure is a cone-shaped ice cream. It is known that its generatrix length is 13cm and its height is 12cm. Then the bottom area of the cone-shaped ice cream is______ ．

As shown in the figure, the generatrix ab of the cone is 13cm, the height Ao of the cone is 12cm, and the bottom radius ob of the cone is R. in RT △ AOB, r = L2 − h2 = 132 − 122 = 5 (CM), s = π R2 = π × 52 = 25 π cm2

It is known that the side expansion of a cone is a sector with a radius of 12 cm and an arc length of 12 π [Pai] cm

Side area: 12 × 12 π / 2 = 72 π≈ 226.2 square cm bottom radius: 12 π / 2 π = 6 cm height = √ (12 - 6) = 6 √ 3 ≈ 10.4 cm side area of cone = 1 / 2 LR = 72 π

As shown in the figure, a fan-shaped thin iron sheet with an arc length of 18.84 decimeters can be enclosed into a cone with a height of 4 decimeters. Try to find the volume of the cone. (the joint is ignored)

13 × 3.14 × 2 × 4, = 13 × 3.14 × 32 × 4, = 3.14 × 12, = 37.68 (cubic decimeter). A: the volume of a cone is 37.68 cubic decimeter