Question

Question 6
From a solid cube of side 7 cm, a conical cavity of height 7 cm and radius 3 cm is hollowed out. Find the volume of the remaining solid.

Answer 1

Given, that , side of a solid cube (a) = 7 cm
Height of conical cavity i.e cone h = 7 cm


Since the height of conical cavity and the side of the cube is equal that means the conical cavity fit vertically in the cube.

The radius of conical cavity i.e cone. r = 3 cm
$\Rightarrow Diameter=2\times r=2\times 3=6cm$

Since the diameter is less than the side of a cube that means the base of a conical cavity does not fit in the horizontal face of the cube.
Now, volume of cube $=(side{)}^3=a^3=(7{)}^3=343c{m}^3$
And volume of conical cavity i.e . cone $=\frac{1}{3}\pi \times r^2\times h$
$=\frac{1}{3}\times \frac{22}{7}\times 3\times 3\times 7$
$=66c{m}^3$
$\therefore$ Volume of remaining solid= Volume of cube – Volume of conical cavity.
$=343–66=277c{m}^3$
Hence, the required volume of solid is $277c{m}^3$