# Question #220cf

Feb 2, 2017

We need the formula for the volume of a cone...........and of course I had to look this up.

#### Explanation:

$\text{Volume of a cone"=1/3xxpixx"radius"^2xx"height}$

$= \frac{1}{3} \times \pi \times {\left(10 \cdot c m\right)}^{2} \times 40 \cdot c m = 4189 \cdot c {m}^{3}$

And thus on immersion in water it displaces a mass of $4189 \cdot g$ of water, and $6283 \cdot g$ of citric acid solution.

And now we work out the mass of the glass used,

$\text{Mass}$ $=$ $\text{volume of glass "xx" density}$

$= 45 \cdot c m \times 60 \cdot c m \times 0.5 \cdot c m \times 2.4 \cdot g \cdot c {m}^{-} 3 =$

$1350 \cdot c {m}^{3} \times 2.4 \cdot g \cdot c {m}^{-} 3 = 3240 \cdot g$

And since the cone displaces a greater mass of water than the mass of the cone, the beast should float, because there is a net buoyant force upwards in water or in citric acid.

I like this question, so I am stealing it for A2 physics...........