The sector (shaded segment + triangle) makes up 1/3 of the circle (which is evident from the fact that the labeled arc measures 120° and a full circle measures 360°). The circle has radius 96 cm, so its total area is π (96 cm)² = 9216π cm². The area of the sector is then 1/3 • 9216π cm² = 3072π cm².
The triangle is isosceles since two of its legs coincide with the radius of the circle, and the angle between these sides measures 120°, same as the arc it subtends. If b is the length of the third side in the triangle, then by the law of cosines
b² = 2 • (96 cm)² - 2 (96 cm)² cos(120°) ⇒ b = 96√3 cm
Call b the base of this triangle.
The vertex angle is 120°, so the other two angles have measure θ such that
120° + 2θ = 180°
since the interior angles of any triangle sum to 180°. Solve for θ :
2θ = 60°
θ = 30°
Draw an altitude for the triangle that connects the vertex to the base. This cuts the triangle into two smaller right triangles. Let h be the height of all these triangles. Using some trig, we find
tan(30°) = h / (b/2) ⇒ h = 48 cm
Then the area of the triangle is
1/2 bh = 1/2 • (96√3 cm) • (48 cm) = 2304√3 cm²
and the area of the shaded segment is the difference between the area of the sector and the area of the triangle:
3072π cm² - 2304√3 cm² ≈ 5660.3 cm²
Answer:
<u> 105</u> students could prefer kiwi if there are 357 total students.
Step-by-step explanation:
Given:
The ratio of students who prefer pineapple to students who prefer kiwi is 12 to 5.
Now, to find number of students prefer kiwi if there are 357 total students.
Let the students prefer pineapple be 
And the students prefer kiwi be 
Total students = 357.
So, we set an equation to get the number of students who prefer kiwi.
According to question:


<em>Dividing both sides by 17 we get:</em>

<em>Thus, students prefer kiwi are:</em>


Therefore, 105 students could prefer kiwi if there are 357 total students.
Answer:
105 boys
Step-by-step explanation:
At a local preschool there is a ratio of 3 boys to 4 girls.
i.e boys:girls = 3:4
There are 245 preschoolers enrolled.
Number of boys =
× 245 = 105 boys
Answer:
Step-by-step explanation:
There is no fractional or decimal part. And no negatives. 1/3 = 0.33333333 with 3 keep repeating. If you want to round it to the nearest whole number, it is 0