Answer:
Radius of P = 5 cm
Explanation:
Radius (r) of Q = 20 cm
Area of Q = 4 × Area of P
This means that:
Area of the quarter circle (Q) = 4 × Area of the circle (P)
Thus:
¼(πr²) = 4 × πr²
Plug in the values into the equation
¼(π*20²) = 4 × πr²
Find the value of r, which is the radius of P
¼(400π) = 4πr²
Multiply both sides by 4
400π = 4πr²*4
400π = 16πr²
Divide both sides by 16π
400π/16π = r²
25 = r²
Take the square root of both sides
√25 = √r²
5 = r
r = 5
Therefore, the radius of P = 5 cm