Question

The cone shaped room has a height of \[15ft\] and a radius of \[72ft\]. How do you find the volume of the room?

Answer 1

Hint: The question asks us to find the volume of the given cone room. We know that, volume of the cone is \[\dfrac{1}{3}\pi {{r}^{2}}h\]. We are given that, radius of the room is \[72ft\], that is, \[r=72ft\] and the height of the room is \[15ft\], that is, \[h=15ft\]. So, we will substitute these given values in the formula of the volume of the cone. Hence, we will get the volume of the room.

Complete step by step answer:
According to the question given to us, we are given a cone shaped room. And it is given that the height of the room is \[15ft\] and the radius of the room is \[72ft\]. And we have to find the volume of the room.

We know that, volume of the cone \[=\dfrac{1}{3}\pi {{r}^{2}}h\] -----(1)
So, if we substitute the given values in the formula of the volume of the cone, then we will have the volume of the room.
Here,
\[r=72ft\] and
\[h=15ft\]
Now, we will substitute these in the equation (1), we will get,
Volume of the cone \[=\dfrac{1}{3}\pi {{r}^{2}}h\]
\[\Rightarrow \dfrac{1}{3}\pi {{\left( 72ft \right)}^{2}}\left( 15ft \right)\]
We will simplify it further, we get,
\[\Rightarrow \dfrac{1}{3}\pi \left( 72\times 72\times 15 \right)f{{t}^{3}}\]
Now, we will divide 15 by 5 and simplify it further, we will get,
\[\Rightarrow \left( 72\times 72\times 5 \right)\pi f{{t}^{3}}\]
On calculating the expression, we get the value as,
\[\Rightarrow 25920\times 3.14f{{t}^{3}}\]
\[\Rightarrow 81388.8f{{t}^{3}}\]

Therefore, the volume of the room is \[81388.8f{{t}^{3}}\].

Note: Since, the room is in the shape of a cone, so calculating the volume of the cone with the given values is the same as the volume of the room. The formula should be written correctly and should not be confused with the formula for volume of cylinder which is, \[\pi {{r}^{2}}h\], and as we can see it is almost similar. Also, while substituting the values in the formula, it should be done step wise.