A cylinder has a diameter of 80 cm and a length of 45 cm. Another cylinder has the same volume but is 80cm long. What is the diameter of the longer cylinder?
don't known
Ah, mathematics, the art of turning numbers into mind-boggling puzzles! Let's solve this one, shall we?
First, we need to find the volume of the original cylinder. The formula for the volume of a cylinder is πr²h, where r is the radius and h is the height.
Given that the diameter of the first cylinder is 80 cm, we can find the radius by dividing it by 2, which gives us 40 cm.
So, the volume of the original cylinder is π * (40 cm)² * 45 cm.
Now, here's the kicker. We want to find the diameter of the longer cylinder, but we already know that its volume is the same as the original cylinder. Therefore, we can set up an equation:
π * (40 cm)² * 45 cm = π * (d/2)² * 80 cm.
Let's simplify that a bit:
(40² * 45) = ((d/2)² * 80).
Now we can solve for d:
(40² * 45) / 80 = (d/2)².
Are you ready for the punchline? Drum roll please...
After performing the calculations, we find that the diameter (d) of the longer cylinder is approximately 56.57 cm.
Remember, my friend, math can be a tricky clown sometimes, but with a little humor and patience, it can be quite entertaining!
To find the diameter of the longer cylinder, we first need to calculate the volume of the given cylinder and then use that volume to find the diameter of the longer cylinder.
Given information:
Diameter of the first cylinder = 80 cm
Length of the first cylinder = 45 cm
Length of the second cylinder = 80 cm
Step 1: Find the volume of the first cylinder
The volume of a cylinder can be calculated using the formula V = π * r^2 * h, where V is the volume, π is a mathematical constant (approximately 3.14), r is the radius of the cylinder, and h is the height or length of the cylinder.
Since the diameter of the first cylinder is given, we can use the formula to find the radius (r). The radius is half of the diameter, so r = 80 cm / 2 = 40 cm.
Now, substitute the values of r and h into the volume formula:
V1 = π * (40 cm)^2 * 45 cm
Step 2: Find the volume of the second cylinder
The volume of the second cylinder is the same as the volume of the first cylinder.
V1 = V2
Step 3: Calculate the diameter of the second cylinder
To find the diameter (d) of the second cylinder, we need to rearrange the volume formula:
V = π * r^2 * h
=> π * r^2 * h = π * (d/2)^2 * h
Now, substitute the known values:
V1 = V2
=> π * (40 cm)^2 * 45 cm = π * (d/2)^2 * 80 cm
Simplify the equation:
(40 cm)^2 * 45 cm = (d/2)^2 * 80 cm
Now, solve for d:
(d/2)^2 = (40 cm)^2 * 45 cm / 80 cm
(d/2)^2 = (40 cm * 40 cm) * (45 cm / 80 cm)
(d/2)^2 = (1600 cm^2) * (0.5625)
(d/2)^2 = 900 cm^2
Taking the square root of both sides:
d/2 = √(900 cm^2)
d/2 = 30 cm
Finally, multiply both sides by 2:
d = 60 cm
Therefore, the diameter of the longer cylinder is 60 cm.
Volume of cylinder
= πr²h
= π(80/2)²*45
= 72000π
Volume of the other cylinder = 72000π
= π(diameter/2)²*80
Solve for diameter in
72000π = π (diameter/2)²*80
I get diameter=60.
V=([d^2*pi)/4] *L
[(80^2*pi)/4]*45=[(d^2*pi)/4]*(45+80)
Multipy both sides of this equation with(4/pi)
(80^2)*45=d^2*(45+80)
6400*45=d^2*125
288000=d^2*125
Divide both sides with 125
288000/125=d^2
2304=d^2
d=sqroot(2304)
d=48 cm