A cube 5.0 cm on each side is made of a metal alloy. After you drill a cylindrical hole 2.0 cm in diameter all the way through and perpendicular to one face, you find that the cube weighs 6.30 N. (a) What is the density of this metal? (b) What did the cube weigh before you drilled the hole in it?
Solution 2E Step 1 of 7: In the given problem, a cube of side a= 5 cm with volume V made of alloy is drilled 1 with a cylindrical hole of diameter d= 2cm through and perpendicular to one face, with cylinder volume V and the cube volume reducing to V resulting in weight of W= 6.3 2 N after drilling. Here in part (a) we need to find the density of the metal by calculating the cube volume after drilling and mass. In part(b) we need to find the weight of cube before drilling using the density and volume of cube . Step 2 of 7: Given data, Side of cube, a=5 cm =0.05 m Diameter of cylindrical hole,d= 2 cm=0.02 m Radius of cylindrical hole, r=d/2 =0.01 m Length of cylindrical hole, L=a=0.05 m Weight of the cube after drilling, W=6.3 N To find, Volume of cube before drilling, V =1 Volume of cylindrical section, V =2 The new volume of cube after drilling, V=V V1= 2 (a)Density of metal alloy, = (b)Weight of cube before drilling, F =g Step 3 of 7: (a) What is the density of this metal To calculate Volume of cube before drilling V = a 3 1 3 Substituting a= 0.05 m V 1 (0.05 m) 4 3 V 1 1.25 × 10 m Step 4 of 7: To calculate Volume of cylindrical section Volume of the cylinder of radius r and length L, V = r L 2 2 Substituting r=0.01 m and L=0.05 m 2 V =23.14(0.01m) (0.05m) V = 0.157 × 10 m 4 3 2