# An ice cream ball of diameter 6cm. is placed over a cone of radius 2.5cm. and height 10cm.. Is the cone big enough to hold all the ice cream if it melts?

Apr 28, 2017

No.

#### Explanation:

To find the area of the first sphere, us the formula $A = 4 \cdot \pi \cdot {r}^{2}$
$A = 4 \cdot \pi \cdot {3}^{2}$
$A = 113.1 c {m}^{2}$
That is the area of the "ice cream scoop."

To find the area of the cone use the formula
A=πrl+πr2 ............($l = \sqrt{{r}^{2} + {h}^{2}}$)
$A = 100.6 c {m}^{3}$
That is the area of the "cone."

Scoop Area: $113.1 c {m}^{3}$
Cone Area: $100.6 c {m}^{3}$

Apr 28, 2017

The cone is not big enough to hold all the ice cream if it melts.

#### Explanation:

As volume of a sphere with radius $r$ is $\frac{4}{3} \pi {r}^{3}$,

and diameter of sphere is $6$ $c m .$ (i.e. radius $3$ $c m .$)

its volume is $\frac{4}{3} \pi \times {3}^{3} = 36 \pi$

Volume of a cone of radius $r$ and height is $h$ is $\frac{1}{3} \pi {r}^{2} h$.

Diameter of cone is $5$ $c m .$ i.e. radius is $2.5$ $c m .$ and its height is $10$ $c m .$,

its volume is $\frac{1}{3} \pi \times {2.5}^{2} \times 10 = \frac{62.5}{3} \pi = 20.8333 \pi$

As it is less then $36 \pi$, the volume of scoop of ice-cream,

the cone is not big enough to hold all the ice cream if it melts.