Acone fits inside a square pyramid as shown. for every cross section, the ratio of the area of the circle to the area of the square is πr^2/4r^ or π/4. a cone is inside of a pyramid with a square base. the cone has a height of h and a radius of r. the pyramid has a base length of 2 r.
since the area of the circle is π/4 the area of the square, the volume of the cone equals
a) π/4 the volume of the pyramid or π/4((2r)(h)/3) or 1/6πrh.
b) π/4 the volume of the pyramid or π/4((2r)^2(h)/3) or 1/3πr^2h.
c) π/2 the volume of the pyramid or π/2((2r)^2(h)/3) or 2/3πr^2h.
d) π/4 the volume of the pyramid or π/4((2r)^2(h)/3) or 1/3πr^2h.