A machinist drilled a cone-shaped hole into a solid cube of metal as shown. If the cube's sides have a length of 4 centimeters, what is the volume of the metal cube after the cone is drilled? Use 3.14 for pi and round your answer to the nearest tenth.

Question

anonymous · Answer

attachment

jim_thompson5910 · Answer

what is the volume of the cube?

jim_thompson5910 · Answer

ignore the cone for now

anonymous · Answer

That's all the question gave me

jim_thompson5910 · Answer

I know, how would you use the given info to find the volume of the cube?

anonymous · Answer

I don't know, tis why im asking for help. if I can get the problem down I can figure it out

jim_thompson5910 · Answer

the cube has side lengths of 4 cm

jim_thompson5910 · Answer

so s = 4

you plug that into the formula

V = s^3

jim_thompson5910 · Answer

V = s^3 is the volume of a cube formula

s = side length
V = volume

jim_thompson5910 · Answer

V = s^3

V = 4^3 .. replace s with 4 (since s = 4)

V = ____ fill in the blank

anonymous · Answer

Whats the ^

jim_thompson5910 · Answer

^ means exponent

jim_thompson5910 · Answer

4^2 = 4 squared

4^3 = 4 cubed

etc etc

anonymous · Answer

okay

anonymous · Answer

I got 64

jim_thompson5910 · Answer

good, 4^3 = 64

jim_thompson5910 · Answer

so the volume of the cube is 64 cubic inches

jim_thompson5910 · Answer

this is if there wasn't a hole in it

but there is

jim_thompson5910 · Answer

we now have to calculate the volume of the cone

this cone has a radius of 2 (half of 4 is 2)

the height is 4 (equal to the side length of the cube)

jim_thompson5910 · Answer

V = pi*r^2*h/3  ... volume of a cube formula

V = 3.14*r^2*h/3 ... replace pi with 3.14

V = 3.14*2^2*h/3 ... replace r with 2 (since r = 2)

V = 3.14*2^2*4/3 ... replace h with 4 (since h = 4)

V = _____ fill in the blank

anonymous · Answer

16.74666

jim_thompson5910 · Answer

good

jim_thompson5910 · Answer

to sum things up so far

jim_thompson5910 · Answer

volume of cube:  64 cubic inches

volume of cone:  16.74666 cubic inches

jim_thompson5910 · Answer

the volume we want is equal to the difference of the two (since you're taking out the cone from the cube)


Volume we want = (volume of cube) - (volume of cone)

Volume we want = (64) - (16.74666)

Volume we want = 64 - 16.74666

Volume we want = 47.25334

Volume we want = 47.3 ... round to the nearest tenth

anonymous · Answer

I see what you did now, thanks again!

jim_thompson5910 · Answer

sure thing