A sector of radius 7cm substending an angle 210 at the center of the circle, is used to form a cone calculate to the nearest whole number,the base radius of the cone,the height of the cone, the total surface arc of the cone, volume of the cone, vertical angle of the cone.

Question

Mathematics.

Answer 1

The arc length of the sector becomes the circumference of the base of the cone.
arc = (210)/(360)*14π = 49/6 π cm
let the radius of the circular base be r
2πr = 49/6π
r = 49/12 cm

We can now find the height of the cone:
h^2 + (49/12)^2 = 7^2
h^2 = 4655/144
h = √(4655/144) = appr 5.686

Now you have all the needed data.
Use the formulas given to you for volume etc.

Answer 2

What about the volume of the cone

Answer 3

YES

Answer 4

What is the Volume of the cone

Answer 5

V=1/3×22/7×16×36=101cm

Answer 6

I'm sorry, but that's not correct. The correct formula for the volume of a cone is V = 1/3 * π * r^2 * h, where r is the base radius and h is the height of the cone.

Plugging in the values we have calculated, we get:

V = 1/3 * π * (49/12)^2 * (5.686)
V ≈ 77.2 cm^3

Therefore, the volume of the cone is approximately 77.2 cm^3.

Answer 7

What is then the vertical angle of the cone

Answer 8

To find the vertical angle of the cone, we need to use the formula:

tan(angle) = (opposite side) / (adjacent side)

In this case, the opposite side is the height of the cone (h) and the adjacent side is the radius of the base (r). So, we have:

tan(angle) = h/r
tan(angle) = (5.686) / (49/12)
tan(angle) ≈ 0.734

Now, we need to take the inverse tangent (tan^-1) of 0.734 to find the angle. Using a calculator, we get:

angle ≈ 36.6 degrees

Therefore, the vertical angle of the cone is approximately 36.6 degrees.