A rectangle is of length 8 inches, breath 11 inches and thickness 2 inches. When it is shaped to a cylindrical rod with the diameter is 10m. What is the height of the cylinder?
Don't see how the rectangular parallelopiped (not a rectangle, which is a 2-dimensioanl figure) could be deformed into a cylinder of height 10, but assuming you mean to find the dimensions of a cylinder with equal volume,
volume = 8*11*2 = 176 in^3 = 2884.112 cm^3
volume of rod is pi r^2 * h, so since r = 5m = 500cm,
250000pi h = 2884.112
h = .00367
So, there appears to be a typo in the problem. I wouldn't describe such a figure as a rod.
Well, this is a classic case of "shape-shifting"!
To find the height of the cylindrical rod, we need to consider the volume of the rectangle before and after it's transformed.
The volume of the rectangle can be calculated by multiplying its length, breadth, and thickness, which gives us:
Volume of rectangle = length x breadth x thickness
= 8 inches x 11 inches x 2 inches
= 176 cubic inches
Since the diameter of the cylindrical rod is given as 10 meters, we can find its radius by dividing the diameter by 2:
Radius of cylinder = diameter / 2
= 10m / 2
= 5m
Now, to find the height, we can rearrange the formula for the volume of a cylinder, which is:
Volume of cylinder = π x radius^2 x height
Since we know the volume of the rectangle is equal to the volume of the cylinder, we can set up the equation like this:
Volume of rectangle = Volume of cylinder
176 cubic inches = π x (5m)^2 x height
Now, we need to convert inches to meters, keeping the equation consistent:
1 inch = 0.0254 meters
Plugging in the values, the equation becomes:
176 cubic inches = π x (5m x 0.0254)^2 x height
= π x (0.127m)^2 x height
= 0.0161 x height
Now, let's solve for the height:
height = 176 cubic inches / 0.0161
= 10931.056s ~ 10931 inches
So, the height of the cylindrical rod is approximately 10931 inches. That's one tall cylinder!
To find the height of the cylinder, we can use the formula for the volume of a cylinder:
V = π * r^2 * h
Where V is the volume, r is the radius, and h is the height.
Given that the diameter of the cylindrical rod is 10m, we can find the radius by dividing the diameter by 2:
r = 10m / 2 = 5m
Now we need to convert the dimensions of the rectangle to meters.
Length of the rectangle = 8 inches = 8 inches * 0.0254m/inch = 0.2032m
Breath of the rectangle = 11 inches = 11 inches * 0.0254m/inch = 0.2794m
Thickness of the rectangle = 2 inches = 2 inches * 0.0254m/inch = 0.0508m
Next, we can find the volume of the rectangle:
Volume of the rectangle = Length * Breath * Thickness
= 0.2032m * 0.2794m * 0.0508m
= 0.002263 m^3
Since the volume of the rectangle equals the volume of the cylinder, we can set:
Volume of the cylinder = π * r^2 * h
= 0.002263m^3
Solving for h:
h = (0.002263m^3) / (π * (5m)^2)
= (0.002263m^3) / (π * 25m^2)
≈ 0.0363m
Therefore, the height of the cylinder is approximately 0.0363 meters.
To find the height of the cylinder, we need to calculate the volume of the rectangle and then equate it to the volume of the cylinder.
First, let's calculate the volume of the rectangle. The volume of a rectangular solid can be found by multiplying its length, width, and height. In this case, the length of the rectangle is 8 inches, the breadth is 11 inches, and the thickness is 2 inches.
Volume of the rectangle = length * breadth * thickness
= 8 inches * 11 inches * 2 inches
Next, we have to convert the volume of the rectangle to the same unit as that of the cylinder's height, which is meters. To do that, we must convert the inches to meters. Since 1 inch is equal to 0.0254 meters, we can convert the volume accordingly.
Volume of the rectangle = (8 inches * 0.0254 meters/inch) * (11 inches * 0.0254 meters/inch) * (2 inches * 0.0254 meters/inch)
Now, we can equate the volume of the rectangle to the volume of the cylinder. The volume of a cylinder can be calculated using the formula:
Volume of the cylinder = π * (radius)^2 * height
Since the diameter of the cylinder is given as 10 meters, we can find the radius by dividing it by 2. Radius = diameter / 2 = 10 meters / 2 = 5 meters.
Let's denote the height of the cylinder as h. The volume of the rectangle should be equal to the volume of the cylinder:
(8 inches * 0.0254 meters/inch) * (11 inches * 0.0254 meters/inch) * (2 inches * 0.0254 meters/inch) = π * (5 meters)^2 * h
Now we need to solve this equation for h to find the height of the cylinder.