Question

The volume of ice-cream in the cone is half the volume of the cone. The cone has a 3 cm radius and

Answer 1

Answer:

h = 5 cm

Step-by-step explanation:

Given that,

The volume of ice-cream in the cone is half the volume of the cone.

Volume of cone is given by :

$V_c=\dfrac{1}{3}\pi r^2h$

r is radius of cone, r = 3 cm

h is height of cone, h = 6 cm

So,

$V_c=\dfrac{1}{3}\pi (3)^2\times 6\\\\V_c=18\pi\ cm^3$

Let $V_i$ is the volume of icecream in the cone. So,

$V_i=\dfrac{18\pi}{2}=9\pi\ cm^3$

Let H be the depth of the icecream.

Two triangles formed by the cone and the icecream will be similiar. SO,

$\dfrac{H}{6}=\dfrac{r}{3}\\\\r=\dfrac{H}{2}$

So, volume of icecream in the cone is :

$V_c=\dfrac{1}{3}\pi (\dfrac{h}{2})^2(\dfrac{h}{3})\\\\9\pi=\dfrac{h^3}{12}\pi\\\\h^3=108\\\\h=4.76\ cm$

or

h = 5 cm

So, the depth of the ice-cream is 5 cm.