Question

I have a snow globe with a radius of $2cm$. How do you find the volume of the globe?

Answer 1

Hint: In this question, we have a snow globe which is technically in the form of a sphere therefore; we will use the formula of the volume of the sphere. On doing some simplification we get the required solution.

Formula used: $v = \dfrac{4}{3}\pi {r^3}$ Where $v$ is the volume of the sphere and $r$ is the radius of the sphere

Complete step-by-step solution:
We have the radius of the globe as $2cm$ therefore, $r = 2cm$
Now to find the area, we will substitute the value of the radius of the globe in the volume formula of a sphere, on substituting the value of $r = 2cm$, we get:
$ \Rightarrow v = \dfrac{4}{3}\pi {(2)^3}$
Now on taking the cube value, we get:
$ \Rightarrow v = \dfrac{4}{3}\pi \times 8$
We know the value of $\pi = 3.14$ therefore, on substituting it in the expression, we get:
$ \Rightarrow v = \dfrac{4}{3} \times 3.14 \times 8$
Now on multiplying all the terms in the numerator using a calculator, we get:
$ \Rightarrow v = \dfrac{{100.48}}{3}$
On dividing the expression, we get:
$ \Rightarrow v = 33.51c{m^3}$

The volume of the globe is equal to $33.51c{m^3}$.

Note: It is to be remembered that the snow globe referred to in this question is a three-dimensional sphere. The volume of a three-dimensional object is the total space it occupies in space.
It is to be remembered that the surface area of a sphere and its volume represent different quantities, unlike the volume, the surface area represents the total area which the sphere would have if it was opened up on a two-dimensional surface.
The formula of the surface area is $sa = 4\pi {r^2}$ where, $s$ is the total surface area of the sphere and $r$ is the radius of the sphere which is half times the diameter $d$.