The radius of a sphere is given by the formula:
r = (0.75 V/) 1/3
where V is its volume. Find the radius of a spherical tank that has a volume of 32 /3 cubic meters.
The radius of a sphere is given by the formula:
r = (0.75 V/) 1/3
where V is its volume. Find the radius of a spherical tank that has a volume of 32 /3 cubic meters.
Hi -
You need to understand two techniques here:The radius of a sphere is given by the formula:
r = (0.75 V/) 1/3
where V is its volume. Find the radius of a spherical tank that has a volume of 32 /3 cubic meters.
- How to handle formulae that involve fractions
- How to handle fractional powers like1/3.
First, write 0.75 as a fraction: $\displaystyle \frac{3}{4}$.
So our formula begins with a fraction which has 3 on the top (numerator) and 4 on the bottom (denominator). If there are any other fractions involved in the formula, bits of them will go along with the 3 in the numerator and other bits with the 4 in the denominator.
So when we come to plug in the value of V, which is $\displaystyle \frac{32\pi}{3}$, we shall put its numerator $\displaystyle 32\pi$ alongside the 3, and its denominator 3 alongside the 4. Like this: $\displaystyle \frac{3\times32\pi}{4\times3}$.
Next, what about the /$\displaystyle \pi$ in the formula? Well, the / tells you that this goes in the denominator of the fraction. Like this: $\displaystyle \frac{3\times32\pi}{4\times3\times\pi}$
So, when we put the power 1/3 outside we get the formula: $\displaystyle r=\left(\frac{3\times32\pi}{4\times3\times\pi}\rig ht)^\frac{1}{3}$
The only other thing you need to know is what the power 1/3 means. Well, it means find the cube root. In other words, find the number which, when cubed (multiplied by itself, and then multiplied by itself again) gives you the number you started with. For example, the cube root of 1000 is 10, because 10 x 10 x 10 = 1000.
So, to work out the value of r you need to:
- Simplify the fraction that I've written for you, by cancelling
- Find the cube root of the result.
You should be able to do this without a calculator, because it all cancels to something very simple.
Good luck!
Grandad