Question

The volume of a cone varies jointly as the height of the cone and the area of the base. The volume of a cone with height 30 centimeters and base 14 centimeters squared is 140 centimeters cubed. Find the volume of a cone with height 7 centimeters and base 12 centimeters squared.

Answer 1

Answer:

V₂=28cm³

Step-by-step explanation:

Way 1

The volume of a cone is $V=\frac{\pi r^{2}h}{3}$,  and  h₁ = 30 cm but the base (Ba₁) is 14 cm², so

$V=\frac{Ba.h}{3}$, where Ba= Base area

if h₂=7cm and Ba₂=12cm² then

$V_{1} =\frac{12cm^{2}.7cm}{3}=28cm^{3}$

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

Answer 2

Step-by-step explanation:

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