The base of a square pyramid is inscribed within the base of a cone, and both solids have the same vertex. The volume of the cone is 200 in.3. What is the volume of the square pyramid, to the nearest tenth of a cubic inch?
+128408 Vcone = (1/3) pi r^2 * h
So.....we have
200 = (1/3)pi r^2 * h multiply both sides by 3
600 =pi r^2 * h solve for h
600 /[ pi r^2 ] = h = height of pyramid and cone
The volume of the pyramid = (1/3) side ^2 * h
The base of the pyramid will be a square inscribed on the crcular base of the cone
The radius of the cone = r and the diameter = 2r
So.....the side of the pyramid = 2r/√2 = √2 * r
So.......the volume of the pyramid =
(1/3) ( side)^2 * height
(1/3) (√2 * r)^2 * ( 600 /[pi r^2] ) =
(1/3) ( 2r^2) * 600 /[ pi r^2 ] =
(1/3) (2 * 600) / pi =
400/ pi in^3 ≈ 127.3 in^3
