Question

In the diagram, the height of the cone is 3 times the

radius. The volume of the cone is 343 Pie cm^3?. What is the
height of the cone?

Answer 1

height = 21 cm

Explanation:

`\textsf{Volume of a cone}=\sf (1)/(3) \pi r^2 h \quad\textsf{(where r is the radius and h is the height)}`

Given:

• h = 3r
• Volume = 343π cm³

Substituting given values into the formula and solving for r:

`\implies \sf 343 \pi=(1)/(3) \pi r^2(3r)`

`\implies \sf 343=(1)/(3)\cdot3r^3`

`\implies \sf 343=r^3`

`\implies \sf r=\sqrt[3]{343}`

`\implies \sf r=7\:cm`

As h = 3r, substitute found value of r into the equation and solve for h:

`\implies \sf h = 3r`

`\implies \sf h=3(7)`

`\implies \sf h=21\:cm`