Answer:

Step-by-step explanation:
The picture of the question in the attached figure
step 1
Let
r ---> the radius of the sector
s ---> the arc length of sector
Find the radius r
we know that



solve for r

step 2
Find the value of s

substitute the value of r

step 3
we know that
The area of complete circle is equal to

The complete circle subtends a central angle of 2π radians
so
using proportion find the area of the sector by a central angle of angle theta
Let
A ---> the area of sector with central angle theta

substitute the value of r


Convert to function notation

Hello!
As you can see, we have a radius of 6. If we divide, this means that this is 2.5 radians. To convert radians to degrees we use the formula below.

First of all we divide 180 by pi.
180/

≈57.3
Now we multiply by 2.5
57.3(2.5)=143.25°
Note that the angle we see is obtuse, or greater than 90°.
Therefore, ∠<span>θ</span>≈143.25°
Now we need to convert this back into radians. This can be represented by the equation below.

First we divide pi by 180 then multiply by our angle.

/180(143.25)≈2.5
Therefore, our angle theta is about
2.5 radians.
I hope this helps!
Draw a diagram to illustrate the problem as shown below.
Calculate the volume of the empty cone.
V₁ = (1/3)π*(6 in)²*(10 in) = 120π in³
Calculate the volume of the sphere.
V₂ = (4/3)π*(1.5 in)³ = 4.5π in³
The volume that can be filled with flavored ice is
V = V₁ - V₂ = 115.5π in³ = 362.85 in³
Answer:
The volume is 115.5π in³ or 362.9 in³ (nearest tenth)
Step-by-step explanation:
It's 27/35, so 27/1 * 1/35