Answer:
1107.0213 cm
Explanation:
Assuming this gutter is half a cylinder,
Volume of half a cylinder = 0.5(πr²l)²
where, Volume = 20l, π = 3.142, r = 0.5(11.5) and l = ?
But, the other units are in cm while the Volume is in liters, so let's convert the liters to cm³
It would be easier to convert the liters to m³ then to cm³ rather than converting directly. So,
1000 L = 1 m³
1 L = ?
1 ÷ 1000 = 0.001 m³
1 m³ = 1,000,000cm³
0.001 m³ = ?
0.001 x 1,000,000 = 1000 cm³
So, if 1 L = 1000 cm³
20 L = ?
20 x 1000 = 20,000 cm³
Thus, 20,000 = 0.5(3.142 x 0.5(11.5) x l)
20,000 = 0.5(3.142 x 5.75 x l)
20,000 = 18.0665l
Make l the subject and divide both sides by 18.0665
length = 1107.0213 cm