Question

the cross section of a solid in the form of a cone of height h, and a hemispherical bowl of radius r. the volume of the hemispherical portion is half that of the conical portion. calculate:
1)the ratio r:h
2)the vertical angle of the cone, correct to the nearest degree.
3)the total volume ,correct to three significant figures, of the solid, given that r=3.5cm [take pie=3.142

Answer 1

we know that

2/3 pi r^3 = 1/2 (1/3 pi r^2 h), so
h = 2/3 r
so, r:h = 3:2

arctan(3/2) = 56.31 deg
not quite sure what you mean for part 2, but that should help


v = 2/3 pi r^3 + 1/3 pi r^2 h
= 2/3 pi r^3 + 1/3 pi r^2 (2/3 r)
= 8/9 pi r^3