Question

HELP ASAP THANK YOU!)

In order to hang a block of gold from a chain necklace, a jeweler drilled a hole in the center, 5 mm in diameter the original block of gold.

If the original block of gold was 27 mm long, 8 mm wide, and 12 mm high, find the volume of the remaining piece of gold to the nearest tenth cubic millimeter.

(The answer choices are below)

Answer 1

2061.9
`mm^(3)`

Explanation:

We can see the original shape of the gold block is a cuboid.

Volume of Cuboid = Length x Width x Height

Volume of Original Gold Block = 27mm x 8mm x 12mm =
`2592mm^(3)`

Next, we can see the shape of the cut-out hole is a cylinder.

Volume of Cylinder =
`\pi r^(2) h`

We know that r = 0.5 x diameter = 0.5 x 5 = 2.5mm

Volume of cut-out hole =
`\pi (2.5)^(2) (27)\\` =
`168.75\pi mm^(3)`

Volume of Remaining Gold Block = Volume of Original Gold block - Volume of cut-out hole

=
`2592mm^(3) -168.75\pi mm^(3)`

= 2061.9
`mm^(3)`