This is a question on Subject of the formula and volume of solid shapes
Step by step explanation
V= (πr²h)➗3
Where V=Volume
r= radius
h=height
a.isolating the variable r means making r the subject of the formula (to stand alone)
V= (πr²h)➗3
Multiply both sides by 3
3V = πr²h
Divide both sides by πh
(3V)/πh = r²
(3V)➗πh=r²
Take the square root of both sides
√(3V ➗ πh) = r
:• r = √(3V ➗πh)
b.we are needed to find r when the Volume and height is given as 1256cm and 12cm respectively
We could use the initial equation but for easier solution we’ll go for the newly created equation
r= √(3V ➗ πh)
r= √(3x1256) ➗ (πx12)
r= √(3768)➗12π
Since π is not given we might leave our answer as
r = √(3768➗12π)
Or go further since π is a constant of 22/7 or 3.1428
r= √[3768 ➗ 12(22/7)]
r= √3768➗ (264/7)
r= √3768 x (7/264)
Reason : when a numerator and a denominator changes sides , the sign Infront of it changes e.g 4 ➗ (2/7) = 4 x (7/2)
Now moving on
r = √3768 x (7/264)
r = √ (26376 ➗ 264)
r = √ (99.909)
r = 9.995cm
So the value of r is 9.995cm approx.
I hope that helps