Question

An ice cream cone has the radius of base \[2{\text{ }}cm\] and if the height is \[{\text{10 }}cm\], then determine its volume.

Answer 1

Hint: What if you find math problem solving is just like an ice cream. Do you realize the shape of ice cream is just like a cone. Let's revisit the formula of volume of cone which is $\dfrac{1}{3}\pi {{r}^{2}}h$ where r is the radius of the base and h is the height of the cone. It is sometimes said that if the dimension of the cone and cylinder are the same then the volume of the cylinder is 3 times the volume of the cone. Apply Pythagoras theorem to find the lateral height of the cone which is also known as the slant height. Remember the unit of the slant height is same as normal height.

Complete step by step answer:
 As we know the formula of the cone is $\dfrac{1}{3}\pi {{r}^{2}}h$ in which r and h have their usual meaning.
Volume of cone is $\dfrac{1}{3}\pi {{r}^{2}}h$
$\Rightarrow$ Now we have radius of cone is 2 cm and its height is 10 cm
$\Rightarrow$ Volume of the cone is $\dfrac{1}{3}\,\pi\, {{2}^{2}}10$ $m^3$.
= $\dfrac{40}{3}\pi\;m^3$

Hence the volume of ice cream cone is $\dfrac{40}{3}\pi\;m^3$.

Note: Sometimes students are confused with the formula of lateral surface area which is $[L.S.A\,=\,\pi rl]\,$, where l is the slant height of cone and volume of cone. Students mistakenly use the formula of sphere instead of cone and also sometimes students use ${{r}^{3}}$ instead of ${{r}^{2}}$ in the formula of volume. Also don’t write radius and height the same as they are totally different things.