Question

The volume of the cone shown is 5 cubic inches. What is the height of a cone with the same base diameter but a volume of 10 cubic inches?

Answer 1

Answer:

The height of the second cone is 2 h₁.

Step-by-step explanation:

The volume of a cone is:

$V=\pi\ r^{2}\frac{h}{3}$

The volume of the first cone is, V₁ = 5 in³.

The volume of the second cone is, V₂ = 10 in³.

The two cones have the same base diameters.

This implies that the two radii are same, i.e. r₁ = r₂.

Compute the height of the second cone as follows:

   $r_{1}=r_{2}$

$\frac{3\cdot V_{1}}{\pi\ h_{1}}=\frac{3\cdot V_{2}}{\pi\ h_{2}}$

  $\frac{V_{1}}{h_{1}}=\frac{V_{2}}{ h_{2}}$

  $\frac{5}{h_{1}}=\frac{10}{h_{2}}$

  $h_{2}=2\ h_{1}$

Thus, the height of the second cone is 2 h₁.