A hot water cylinder whose length is 1.12m is to hold 200 liters.Find the diameter of the cylinder in millimeters.
since 1L = 1000cm^3,
200000 = pi r^2 * 112
r = 23.8 cm
23.84740
To find the diameter of the cylinder, we can use the formula for the volume of a cylinder:
Volume = π × r^2 × h,
where π is a mathematical constant approximately equal to 3.14159, r is the radius of the cylinder, and h is the height or length of the cylinder.
In this case, we have the height of the cylinder, which is 1.12 meters, and we need to find the diameter in millimeters. To do this, we need to convert the volume from liters to cubic meters.
Since 1 liter is equal to 0.001 cubic meters, we can convert the volume as follows:
Volume = 200 liters × 0.001 cubic meters/liter,
Volume = 0.2 cubic meters.
Now, let's rearrange the volume formula to solve for the radius:
0.2 = π × r^2 × 1.12.
Divide both sides of the equation by π × 1.12:
0.2 / (π × 1.12) = r^2.
Taking the square root of both sides, we get:
r = √(0.2 / (π × 1.12)).
Now, we can calculate the radius:
r ≈ 0.2528 meters.
Finally, to find the diameter, we multiply the radius by 2 and convert it to millimeters:
diameter = 2 × r × 1000,
diameter ≈ 505.6 millimeters.
Therefore, the diameter of the cylinder is approximately 505.6 millimeters.