Two cylinders, A and B, are mathematically similar - OCR - GCSE Maths - Question 19 - 2018 - Paper 4

Calculating the left-hand side: $\frac{2400}{750} = 3.2$ Thus, we have: $3.2 = \left( \frac{12}{h_B} \right)^3$

Taking the cube root of both sides: $\sqrt[3]{3.2} = \frac{12}{h_B}$ This implies: $h_B = \frac{12}{\sqrt[3]{3.2}}$ Calculating the cube root: $\sqrt[3]{3.2} \approx 1.5$ Therefore: $h_B \approx \frac{12}{1.5} \approx 8$

After calculating, we find that the height of cylinder B is approximately 8.1 cm when rounded to an appropriate degree of accuracy.