a piece of string 25 cm long goes exactly once round the edge of a plate in the form of a quadrant pie = 3.14
Find the radius of this quadrant and calculate the area of the quadrant
s = rθ
You have s and θ (hint: a full circle is 2π), so find r.
a = 1/2 r^2 θ
then let 'er rip
and that's pi, not pie!
To find the radius of the quadrant, we know that the circumference of a circle is given by the formula C = 2πr, where C is the circumference and r is the radius. In this case, the length of the string used to go once around the edge of the plate is given as 25 cm.
Since the string goes once around the edge, we can equate the circumference of the circle with the length of the string:
C = 25 cm
Substituting the formula for the circumference, we have:
2πr = 25 cm
Now we can solve for the radius. Divide both sides of the equation by 2π:
r = 25 cm / (2π)
Using the approximation π = 3.14, we can calculate the radius:
r = 25 cm / (2 * 3.14)
r ≈ 3.98 cm
Therefore, the radius of this quadrant is approximately 3.98 cm.
To calculate the area of the quadrant, we know that the formula for the area of a sector (in this case a quadrant) is given by A = (θ/360°) * πr^2, where A is the area, θ is the angle (in degrees), and r is the radius.
Since we have a quadrant, the angle of the sector is 90°. Substituting these values into the formula, we have:
A = (90° / 360°) * π * (3.98 cm)^2
Simplifying, we get:
A = (1/4) * π * (3.98 cm)^2
Using the value of π as 3.14, we can calculate the area:
A ≈ (1/4) * 3.14 * (3.98 cm)^2
A ≈ 3.14 * (15.8404 cm^2)
A ≈ 49.6176 cm^2
Therefore, the area of this quadrant is approximately 49.6176 cm².