Question

I’m confused on this one

Answer 1

From the given diagram, It is clearly visible that a cone (height = 6cm and diameter = 4cm) is cut from a cube (side edge = 6cm). It says to find the volume of the remaining portion (blue section of the solid).
To find the volume of blue section, we must find the difference between volumes of solid cube and cone.

Finding volume of cube,

`cube = {a}^(3) = {6}^(3) = 216 \: {cm}^(3)`
Finding volume of cone,

`cone = (1)/(3) \pi {r}^(2) h = (1)/(3) \pi( {2}^(2) )(6) = 8\pi \: {cm}^(3)`
Finding difference of their volumes,

`cube - cone = 216 - 8\pi = 190.9`
Hence, the volume is approximately 190.9 cubic centimeters.