Answer: (a) 314.2cm², (b) 157.1cm², (c) 78.55cm² (e) 6.77
Step-by-step explanation: (a) Area of the circle with radius of 10 cm = πr²
= 3.142 × 10 × 10
= 3.142 × 100
= 314.2cm²
The formula = πr²
(b) Area of the half of a circle known as semicircle
= πr²/2
= 3.142 ×10 × 10/2
= 3.142 × 50
= 157.1cm²
The formula = πr²/2
(c) A quarter of a circle is called quadrant
= πr²/4
= 3.142 × 10 × 10/4
= 314.2/4
= 78.55cm²
The formula is written thus = πr²/4, which implies that the circle is divided into 4 unit
(d) The conjecture about how to determine the area of the sector is
Formula of a sector = ∅/360(πr²)
Information
The arc cant be 60°, therefore information incomplete.
(e) Area of the sector with the angle AOB of 60° = 24.
To find the radius of the angle, make v the subject of the formula from the formula.
Sector area = πr²∅/360°
equate formula to 24.
Therefore πr²∅/360° = 24
Multiply through by360° to make it a linear expression
It now becomes πr²∅ =24× 360°
r² = 24 x 360/π × ∅°
r² = 24 × 360° /3.142 × 60°
r² = 3,640/188.52
r² = 45.8
To find r , we take the square root of both side by applying laws of indicies
Therefore r = √45 .8
r = 6.77
(f) General formula = ∅°/360° × (πr²)
angle substended at centre by the arc = x°
assuming the radius of the circle = ycm, Therefore, area of the sector = { ∅°/360° × πy² }