From each end of a solid metal cylinder, metal was scooped out in hemispherical form of same diameter. The height of the cylinder is 10 cm and its base is of radius 4.2 cm. The rest of the cylinder is melted and converted into a cylindrical wire of 1.4 cm thickness. Find the length of the wire. [Use pi = 22/7 * J

Sure, let's solve this step by step.

Step 1: Calculate the volume of the original cylinder The formula for the volume of a cylinder is V = πr²h, where r is the radius and h is the height. Here, r = 4.2 cm and h = 10 cm. So, the volume of the cylinder is V = π(4.2)²(10) = 22/7 * 4.2 * 4.2 * 10 = 554.4 cm³.

Step 2: Calculate the volume of the two hemispheres The formula for the volume of a hemisphere is V = 2/3πr³. Here, r = 4.2 cm. So, the volume of one hemisphere is V = 2/3 * π * (4.2)³ = 2/3 * 22/7 * 4.2 * 4.2 * 4.2 = 123.6 cm³. Since there are two hemispheres, the total volume of the two hemispheres is 2 * 123.6 = 247.2 cm³.

Step 3: Calculate the volume of the remaining cylinder The volume of the remaining cylinder is the volume of the original cylinder minus the volume of the two hemispheres. So, the volume of the remaining cylinder is 554.4 - 247.2 = 307.2 cm³.

Step 4: Calculate the length of the wire The remaining cylinder is melted and converted into a cylindrical wire of 1.4 cm thickness. The volume of a cylinder is V = πr²h. Here, the volume is 307.