Given the area of a circle is π divided by 9, find the circumference of the circle One more question, The square of 4x - 25 = 0, find the value of X,

Given the area of a circle is π divided by 9, find the circumference of the circle One more question, The square of 4x - 25 = 0, find the value of X,

two
∵ circle area formula s = π R
two
Take π / 9 and get π / 9 = π R
We get r = 1 / 3
Taking r = 1 / 3 into the circle circumference formula C = 2 π R, we get C = 2 π / 3
If 4x squared - 25 = 0, then 4x squared = 25,
Square of x = 25 / 4
X = 5 / 2

In this paper, a cone-shaped container is enclosed by a sector iron sheet with radius R and central angle X. the volume of the container is expressed as a function of central angle X

Sector arc length C = XR
Radius of cone base circle r = C / (2 π) = XR / (2 π)
Tapered bus = R
Cone height h = √ (R ^ 2-r ^ 2) = √ {R ^ 2 - [XR / (2 π)] ^ 2}
The volume of cone is v = R ^ 2H π / 3
=[xr/(2π)]^2√{r^2-[xr/(2π)]^2}π/3

What is the volume of a conical vessel made of a sector iron sheet with a center angle of 216 ° and a radius of 5cm?

Imagine the process of forming a solid cone. It is not difficult to find that the key to finding the volume is to find out the bottom area and height
The circumference of the bottom surface is equal to the arc length of the iron sheet circle: 5cm * (216 / 360) = = 3cm
Bottom radius: 3cm / 2pi
Bottom area: pi * (3cm / 2pi) ^ 2 = = 9 / (4Pi) cm2
According to the Pythagorean theorem, the height, generatrix and the radius of the bottom of a cone can form a right triangle,
H == Sqrt( ((5cm)^2) - ((3cm)^2) ) == 4cm
Where sqrt () is the root sign
Cone volume
V == (1/3) * ((9/(4Pi)) cm2) * (4cm) == (3/Pi) cm^3
The volume is (3 / PI) cm ^ 3, which is about 0.955 cm ^ 3

A conical vessel is welded with a sector iron sheet with a center angle of 216 ° and a radius of 5 (excluding the weld), then the volume of the vessel is?

Arc length of sector = circumference of cone bottom = 216 π * 5 / 180 = 6 π
Ψ bottom radius = 3
∵ generatrix of cone = 5
The height of the cone = 4
Volume = 1 / 3 * π * 3 ^ 2 * 4 = 12 π (CC)
And the picture of this problem is very simple, I believe you can solve it yourself

If a sector with radius of 10cm and center angle of 216 ° is used to make the side of a cone, the height of the cone is______ cm．

As shown in the figure: the circumference of a circle is the arc length of a sector. The formula n π R180 = 2 π x, and ∵ n = 216, r = 10, ∵ (216 × π × 10) △ 180 = 2 π x is given. The solution is x = 6, H = 102 − 62 = 8. So the answer is: 8cm

What is the height of the cone if a sector with r = 10cm and N = 216 degrees is used as the side of the cone?

Bottom radius / side sector radius = n / 360
So r = 10 * 216 / 360 = 6cm
According to Pythagorean theorem
H = 8cm

It is known that the developed side view of a cone is a sector with a radius of 15 and a center angle of 216 degrees, then the height of the cone is

According to the arc length formula, the circumference of the bottom circle of the cone is calculated, then the radius of the bottom circle is calculated, and then the height is calculated according to the Pythagorean theorem
Arc length: n π R / 180 = 15 × 216 π / 180 = 18 π
The radius of the bottom circle is 9
Cone height & # 178; = 15 & # 178; - 9 & # 178; cone height = 12
I hope my answer will help you

A sector is shown in the figure, the radius is 10cm, the center angle is 270 ° and it is used to make the side of a cone, then the height of the cone is______ cm．

As shown in the figure: the circumference of a circle is the arc length of a sector. The relation n π R180 = 2 π x is listed. Because n = 270, r = 10, so 270 × π × 10180 = 2 π x, the solution is x = 152, H = 100 − 2254 = 1752 = 572cm

If a sector with a center angle of 288 ° and a radius of 10cm is used to form the side of a cone, then the height of the cone is
A.5√3cm B.4 C.5 D6
A. 5 √ 3cm b.8 C.6 d.6 √ 2 wrong, hee hee

C. First, we list the perimeter of the sector: 288 / 360 * 2 * 3.14 * 10; then, we list the ground perimeter of the cone: 2 * 3.14 * r (let R be the radius of the bottom of the cone), and then: because the perimeter of the sector is equal to the perimeter of the bottom, so 288 / 360 * 2 * 3.14 * 10 = 2 * 3.14 * r, the solution is r = 8cm, and because the radius of the sector is 10cm, the bevel length of the cone is 10cm, so according to the Pythagorean theorem, the height of the cone is 6cm, so we choose C

Given that the generatrix length of a cone is 6 & nbsp; cm and the radius of its bottom is 3cm, the center angle of the sector in the side expansion of the cone is calculated

The radius of the bottom of the cone is 3cm, the perimeter of the bottom of the cone is 6 π, let the center angle of the sector be n °, n π × 6180 = 6 π, and the solution is n = 180