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Firstly, a quick overview of rationalising the denominator. For this, we want to make sure that the bottom half of the fraction (the denominator) is rationalised (and so doesn't contain any surds any more...

Multiply both sides by 5: 5x = 3r - 4Add 4 to both sides: 5x + 4 = 3rDivide both sides by 3: (5x + 4)/3 = r

Let radius of cylinder be r. Let height of cylinder be h. We know that the volumes of the hemisphere and cylinder are equal:2(pi)r³/3 = h(pi)r².Multiplying both sides by 3 and dividi...

X=6m

This is a quadratic equation, for these types of questions it is often easiest to try and rearrange the formula into the form ax^2 + bx + c = 0, where a, b and c are whole numbers. Therefore the first thi...