Mathematics Question and Solution
Calculating x.
Notice.
x is the radius of the big inscribed half circle.
Let y be the radius of the small inscribed half circle.
It implies;
2x+2y = 16
2y = 16-2x
y = (8-x) units.
Again, y is the radius of the small inscribed circle.
Therefore, x, radius of the big inscribed half circle is;
Area half circle with radius x units + Area half circle with radius (8-x) units + 15π = Area half circle with radius 8 units.
½(x²)π+½(8-x)²π+15π = ½(8²)π
x²+(8-x)²+30 = 64
x²+64-16x+x²+30 = 64
2x²-16x+30 = 0
x²-8x+15 = 0
x²-3x-5x+15 = 0
x(x-3)-5(x-3) = 0
(x-5)(x-3) = 0
It implies;
x ≠ 3
x = 5 units.
Therefore, y, radius of the small inscribed half circle is;
y = (8-x)
And x = 5 units.
y = 8-5
y = 3 units.
Checking Accuracy.
2x+2y = ?
2*5+2*3 = ?
10+6 = 16
Checked.
