Answer:
V₂=28cm³
Step-by-step explanation:
Way 1
The volume of a cone is [tex]V=\frac{\pi r^{2}h}{3}[/tex], and h₁ = 30 cm but the base (Ba₁) is 14 cm², so
[tex]V=\frac{Ba.h}{3}[/tex], where Ba= Base area
if h₂=7cm and Ba₂=12cm² then
[tex]V_{1} =\frac{12cm^{2}.7cm}{3}=28cm^{3}[/tex]
Way2
If the volume of a cone varies jointly as the height of the cone and the area of the base, then we must find the relationship between the bases and heights of the cones
Ba₁*h₁ = 30cm*14cm² = 420cm³
Ba²*h²= 7cm*12cm² = 84cm³
420/84 = 5; ratio = 5 also
V₂=V₁/5 ⇒ V₂=140cm³/5 = 28cm³
