A sector of a circle of radius 7cm subtending angle 270 degree at the center calculate the area of segment

Answer 1

To calculate the area of the segment, we first need to calculate the area of the sector and the area of the triangle within the sector.

The area of the sector can be calculated using the formula:

Area of sector = (θ/360) x π x r^2

Where:
- θ = angle in degrees = 270
- r = radius = 7 cm

Area of sector = (270/360) x π x 7^2
= (3/4) x π x 49
= 3.375π square cm

Next, we need to calculate the area of the triangle within the sector. The angle at the center of the circle is 270 degrees, so the angle at the circumference of the circle is 90 degrees. This means that the triangle is a right-angled triangle with sides of 7 cm, 7 cm, and the radius of the circle (7 cm).

The area of the triangle can be calculated using the formula:

Area of triangle = 0.5 x base x height
= 0.5 x 7 x 7
= 24.5 square cm

Finally, to find the area of the segment, we subtract the area of the triangle from the area of the sector:

Area of segment = Area of sector - Area of triangle
= 3.375π - 24.5
≈ 5.179 square cm

Therefore, the area of the segment is approximately 5.179 square cm.

Answer 2

your first mistake comes here:
= (3/4) x π x 49
= 3.375π square cm
even a casual glance can show that that is wayyyyy too small!

the area of a segment is
A = 1/2 r^2 (θ - sinθ) = 1/2 * 7 *(3π/2 - sin(3π/2)) =

Answer 3

You are correct, and I apologize for the mistake in my previous calculation. Let's correct it:

A = 1/2 * 7 * (3π/2 - sin(3π/2))
A = 1/2 * 7 * (3π/2 - (-1))
A = 1/2 * 7 * (3π/2 + 1)
A = 21π/4 + 7/2
A = 41.71 square cm

Therefore, the correct area of the segment is 41.71 square cm. Thank you for pointing out the error!