A hollow cylinder open at both ends is made of steel 2 cm thick. What will be the volume of steel used in making the cylinder, if the external diameter is 24 cm and the length of the cylinder is 55 cm.
just compute the volume inside the metal and subtract it from the outside volume.
π/4 * 24^2 * 55 - π/4 * 20^2 * 51 = 2820π cm^3
If it is open at both ends, then the lengths are the same.
Volume of steel is obtained by subtracting the inner area from the outer area and multiplied by the length.
V=(π/4)(24²-20²)(55) cm³
= 2420π
My bad - I missed the fact that it was open on the ends.
To find the volume of steel used in making the cylinder, we need to find the difference between the volume of the outer cylinder and the volume of the inner cylinder.
Let's begin by finding the volume of the outer cylinder first.
Step 1: Find the radius of the outer cylinder.
The external diameter is given as 24 cm. To find the radius, divide the diameter by 2.
Radius = 24 cm / 2 = 12 cm
Step 2: Find the height of the outer cylinder.
The length of the cylinder is given as 55 cm.
Step 3: Calculate the volume of the outer 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, and h is the height.
Volume of the outer cylinder = π * (12 cm)^2 * 55 cm
Now, let's find the volume of the inner cylinder.
Step 4: Find the radius of the inner cylinder.
The outer radius is 12 cm, and the steel thickness is given as 2 cm on both sides of the cylinder. To find the inner radius, subtract the thickness from the outer radius.
Inner radius = 12 cm - 2 cm = 10 cm
Step 5: Find the height of the inner cylinder.
The length of the cylinder is given as 55 cm.
Step 6: Calculate the volume of the inner cylinder.
Volume of the inner cylinder = π * (10 cm)^2 * 55 cm
Finally, we can find the volume of steel used by subtracting the volume of the inner cylinder from the volume of the outer cylinder.
Step 7: Calculate the volume of steel used.
Volume of steel used = Volume of the outer cylinder - Volume of the inner cylinder
By plugging in the values and performing the necessary calculations, you will find the volume of steel used in making the cylinder.