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Question

Find the volume that is left when a hole is drilled through the metal block shown below. Round to the nearest hunderdth

L=18cm

W= 12cm

H=12cm

circle with a line 8cm

Answer 1

The length of cuboid = 18 cm .

height of cylinder (h _cylinder ) = 18 cm .

Width of cuboid (w) = 12 cm .

Height of cuboid (h _cuboid ) = 12 cm .

Volume of cuboid = lbh = lbh_cuboid .

Length of diameter = 8 cm .

Radius of the cylinder (r) = 8/2 = 4 cm .

Volume of cylinder = πr²h .

Volume that is left when a hole is drilled through the metal block = 

    ⇒ (Volume of cuboid) - (Volume of cylinder ) = (lbh _cuboid ) - (πr²h _cylinder)

                                                                ⇒ [18*12*12] - [π(4)² * 18]

                                                                ⇒ 18 [12*12 - π(4)² ]

                                                                ⇒ 18 [93.73 ] = 1687.22 cm³ .

Therefore the volume that is left when a hole is drilled through the metal block is 1687 cm³ .