Given that the generatrix length of the cone is 5 cm and the side area is 15 cm 2, what is the volume of the cone?

Given that the generatrix length of the cone is 5 cm and the side area is 15 cm 2, what is the volume of the cone?

36 No

Calculate the volume of the cone. The radius of the bottom of the cone is 4cm and the height is 5cm

The volume is 3.14 × 4 × 4 × 5 × 1 / 3 = 83.73 cubic centimeter

If the surface area of the cone is 15 П and the center angle of the side view is 60 °, the volume of the cone is

Let R be the bottom radius of the cone, R be the generatrix and H be the height
2πr/R=π/3 --> R=6r
r²+h²=R² --> h=√35 r
Surface area s = π R & sup2; + π R & sup2; / 6 = 7 π R & sup2; = 15 π -- > R = √ 15 / 7
Volume v = 1 / 3 π R & sup2; H = 25 √ 3 π / 7

If the surface area of a cone is 15 π, and the center angle of the side expanded view is 60 °, then the volume of a cone is 15 π
This question I read Baidu a lot of other people answer, there is a puzzling place, is the cone bottom radius r, fan radius L, then 60 π L / 180 = 2 π R, how does this relationship come out? Why is the length of the bus related to the arc length? I don't know, thx~
Why 180 is not 360?

This is because the side view of the cone is fan-shaped: the radius of the fan-shaped is exactly the length of the generatrix of the original cone: the arc length of the fan-shaped = 60 π L / 180 is exactly the circumference of the bottom surface of the cone = 2 π R:

Is y = (x * x + 1) cosx a bounded function

No. because x * x is an increasing function, it can be infinite, and cosx is a periodic function. So let x = 2kpi, let K be infinite, then y is infinite

The function y = 2cos, parenthesis 3 / π * x + 2 / 1 is transformed into y = cosx

How to transform the image of the function y = 2cos (π X / 3 + 1 / 2) to get the image of the function y = cosx? Step 1: function y = 2cos (π / 3x + 1 / 2) = 2cos [π / 3 (x + 3 / 2 π)], move 3 / 2 π units to the right to get the image of y = 2cos (π / 3x); step 2: extend the image of y = 2cos (π / 3x) to π / 3 times of the original image, The third step is to shorten the height of the image of y = 2cosx to 1 / 2 of the original, and finally get the image of y = cosx

The minimum value of the function y = 3 - (cosx-1 / 2) & sup2; is

3/4
Let t = cosx-1 / 2, the value range of cosx is - 1 to 1, when cosx = - 1, the minimum value of Y is 3 / 4

It is known that x belongs to [- π / 6, π / 2]. Find the maximum value of the function y = (SiNx + 1) * (cosx + 1)

y=（sinx+1)(cosx+1）
=sinx+cosx+sinxcosx+1
=√2*sin(x+π/4)+1/2 *sin2x+1
=√2*sin(x+π/4) - 1/2 *cos(2x+π/2) +1
=√2*sin(x+π/4) - 1/2 *[1-2sin²(x+π/4)] +1
=sin²(x+π/4)+√2*sin(x+π/4)+1/2
=[sin(x+π/4)+√2/2]²
Because x ∈ [- π / 6, π / 2], so:
x+π/4∈[π/12,3π/4]
Then when x + π / 4 = π / 2, that is, x = π / 4, the function y has the maximum value of 3 / 2 + √ 2
When x + π / 4 = π / 12, that is, x = - π / 6, the function y has a minimum value of 1 / 2 + √ 3 / 4
❤ your question has been answered ~ (> ^ ω)^

Find the maximum value of the function y = (SiNx cosx) / (SiNx + cosx), X ∈ [- π / 12, π / 12]

y=(sinx-cosx)/(sinx+cosx)
=sin²x-cos²x
=-cos2x
∵x∈【-π/12,π/12】
∴2x∈[-π/6,π/6]
cos2x∈[√3/2,1]
-cos2x∈[-1,-√3/2]
When x = 0, y (min) = - 1
When x = ± π / 12, y (max) = - √ 3 / 2

Find the maximum value of the function y = (1-sinx) (1-cosx)

Expansion, y = sinxcosx + 1-cosx-sinx
Let cosx + SiNx be t, then cosxsinx can also be expressed by T
Then the separation constant can be solved