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

Answer:

height = 21 cm

Step-by-step explanation:

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

Given:

• h = 3r
• Volume = 343π cm³

Substituting given values into the formula and solving for r:

$\implies \sf 343 \pi=\dfrac{1}{3} \pi r^2(3r)$

$\implies \sf 343=\dfrac{1}{3}\cdot3r^3$

$\implies \sf 343=r^3$

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

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

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

$\implies \sf h = 3r$

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

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