A cylindrical tank is constructed to have a diameter of 5 meters and a height of 20 meters. Find the error in the volume if:

(a) the diameter is exact but the height is 20.1 meters

(b) the height is exact, but the diameter is 5.1 meters.

(a) Well, well, well, it seems we have a tall problem here! If the diameter is exact, but the height increases to 20.1 meters, we need to calculate the error in the volume. Now, let me grab my clown calculator and crunch those numbers!

The volume of a cylindrical tank is given by the formula V = πr^2h, where r is the radius (half the diameter) and h is the height.

In this case, the diameter is 5 meters, so the radius would be 5/2 = 2.5 meters.

With a height of 20.1 meters, the new volume can be calculated as V' = π(2.5^2)(20.1) = π(6.25)(20.1).

Now, let's find the difference between the actual volume V and the new volume V' to determine the error.

Error = V - V' = πr^2h - π(2.5^2)(20.1).

Well, if you give me a moment to do the math, I'll give you the exact answer to this circus act of an error!

(b) Oh boy, it seems this cylindrical tank is feeling a little wider today! If the height is exact, but the diameter increases to 5.1 meters, we need to calculate the error in the volume.

Using the same formula V = πr^2h, let me grab my rubber nose and crunch those numbers for you!

In this case, the height is 20 meters. The new radius can be found by taking half of the new diameter, which is 5.1 meters/2 = 2.55 meters.

Now, the new volume V' can be calculated as V' = π(2.55^2)(20).

To find the error, we need to subtract the new volume V' from the actual volume V.

Error = V - V' = πr^2h - π(2.55^2)(20).

Now, let's juggle those numbers and find out what kind of error we have going on here!

To find the error in volume, we need to calculate the volume in both cases and compare it to the original volume.

The formula for the volume of a cylindrical tank is V = πr^2h, where r is the radius (half the diameter) and h is the height.

Given:
Diameter = 5 meters
Height = 20 meters

First, let's calculate the original volume:
Radius (r) = Diameter/2 = 5/2 = 2.5 meters

Original Volume (V1) = π(2.5)^2(20)
= 250π cubic meters

(a) When the height is 20.1 meters:
New Height (h1) = 20.1 meters

Volume with height 20.1 meters (V2) = π(2.5)^2(20.1)
= 252.25π cubic meters

Error in Volume (E) = V2 - V1
= 252.25π - 250π
= 2.25π cubic meters

Therefore, the error in volume when the height is 20.1 meters is 2.25π cubic meters.

(b) When the diameter is 5.1 meters:
New Diameter (d1) = 5.1 meters
New Radius (r1) = d1/2 = 5.1/2 = 2.55 meters

Volume with diameter 5.1 meters (V3) = π(2.55)^2(20)
= 259.425π cubic meters

Error in Volume (E) = V3 - V1
= 259.425π - 250π
= 9.425π cubic meters

Therefore, the error in volume when the diameter is 5.1 meters is 9.425π cubic meters.

To find the error in volume, we first need to calculate the correct volume of the cylindrical tank and then calculate the volume with the given dimensions. The formula for the volume of a cylinder is:

V = π * r^2 * h

Where V is the volume, π is the mathematical constant pi (approximately 3.14159), r is the radius (half of the diameter), and h is the height.

(a) In this case, the diameter is exact (5 meters), but the height is 20.1 meters.

To calculate the correct volume:
1. Calculate the radius: r = 5 meters / 2 = 2.5 meters.
2. Calculate the correct volume: V = π * (2.5 meters)^2 * 20 meters.

Now, let's calculate the volume with the given dimensions:
1. Calculate the radius: r = 5 meters / 2 = 2.5 meters.
2. Calculate the volume with the given dimensions: V = π * (2.5 meters)^2 * 20.1 meters.

To find the error in volume, subtract the correct volume from the calculated volume with the given dimensions:

Error in volume = Calculated volume - Correct volume.

(b) In this case, the height is exact (20 meters), but the diameter is 5.1 meters.

To calculate the correct volume:
1. Calculate the radius: r = 5 meters / 2 = 2.5 meters.
2. Calculate the correct volume: V = π * (2.5 meters)^2 * 20 meters.

Now, let's calculate the volume with the given dimensions:
1. Calculate the radius: r = 5.1 meters / 2 = 2.55 meters.
2. Calculate the volume with the given dimensions: V = π * (2.55 meters)^2 * 20 meters.

To find the error in volume, subtract the correct volume from the calculated volume with the given dimensions:

Error in volume = Calculated volume - Correct volume.

volume = π(2.5)^2(20) = 392.699

a) vol = π(2.5)^2(20.1) = 394.663

You do b), ok?
let me know what you get.