From of cylindrical bar of diameter 14 cm with the length of 8 cm, how many spherical balls of radius 1 cm are made for manufacturing of ball bearings ?
Question
From of cylindrical bar of diameter 14 cm with the length of 8 cm, how many spherical balls of radius 1 cm are made for manufacturing of ball bearings ?
Solution
Sure, let's solve this step by step:
Step 1: First, we need to find the volume of the cylindrical bar. The formula for the volume of a cylinder is πr²h, where r is the radius and h is the height. The diameter of the cylinder is given as 14 cm, so the radius would be half of that, which is 7 cm. The height is given as 8 cm. So, the volume of the cylindrical bar is π*(7 cm)²*(8 cm) = 1232 cm³.
Step 2: Next, we need to find the volume of a spherical ball. The formula for the volume of a sphere is 4/3πr³, where r is the radius. The radius of the spherical ball is given as 1 cm. So, the volume of the spherical ball is 4/3π*(1 cm)³ = 4.19 cm³.
Step 3: Finally, we need to find out how many spherical balls can be made from the cylindrical bar. This can be found by dividing the volume of the cylindrical bar by the volume of a spherical ball. So, 1232 cm³ / 4.19 cm³ = approximately 294.
Therefore, approximately 294 spherical balls of radius 1 cm can be made from a cylindrical bar of diameter 14 cm and length 8 cm.
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