The diagram shows a cone inscribed in a hemisphere. What is the ratio of the volume of the cone to the volume of the hemisphere?
a. 1:3
b. 2:3
c. 1:2
d. More information needed
Volume of hemisphere = $$\frac12\times\frac43\times\pi\times r^3$$
$$=\frac23\pi r^3$$
Volume of cone = $$\frac13\times\pi\times r^2\times h$$
since h = r
V =$$\frac13\times\pi\times r^2\times r$$
$$=\frac13\pi r^3$$
Ratio of volume of Cone to volume of Hemisphere
$$\frac13\pi r^3:\frac23\pi r^3$$
$$\frac13:\frac23$$ × both sides by 3
C 1:2