A cylindrical jug that carries 5 litres of water when filled to the brim , has a height of 20cm. Determine the diameter of the base surface of jug ( in cm ) round off the answer to the nearest integer.
recall that v = πr^2 h, so
πr^2*20 = 5000
r^2 = 250/π
so the diameter d = 2√(250/π)
250
To determine the diameter of the base surface of the cylindrical jug, we can use the formula for the volume of a cylinder:
V = πr²h
Where V is the volume of the cylinder, r is the radius of the base, and h is the height of the cylinder.
In this case, the volume of the jug when filled to the brim is 5 litres, or 5000 cubic centimeters. The height of the jug is given as 20cm. Therefore, we can rearrange the formula to solve for the radius:
5000 = πr² * 20
Dividing both sides by 20π:
r² = 5000 / (20π)
Calculating the value:
r² ≈ 79.577
Taking the square root to find the radius:
r ≈ √79.577
r ≈ 8.918
Finally, to find the diameter, we multiply the radius by 2:
d ≈ 2 * 8.918
d ≈ 17.836
Rounding off the answer to the nearest integer:
d ≈ 18 cm
Therefore, the diameter of the base surface of the jug is approximately 18 cm.