3
The market value of a certain precious stone varies directly as the square of its mass. One such stone of mass $10 \mathrm{~kg}$ has a value of $\mathrm{Ksh} 600000$.
Calculate the value of a similar stone whose mass is $18.5 \mathrm{~kg}$.
(3 marks)

Step 1 ：Given that the market value of the precious stone is directly proportional to the square of its mass, we can write the relationship as: \(V = k \times M^2\), where V is the market value, M is the mass, and k is the constant of proportionality.

Step 2 ：We are given that a stone of mass 10 kg has a value of Ksh 600,000. We can use this information to find the value of k: \(k = \frac{V}{M^2} = \frac{600000}{10^2} = 6000\).

Step 3 ：Now that we have the value of k, we can use it to find the value of a similar stone whose mass is 18.5 kg. We can plug in the mass of the second stone into the equation \(V = k \times M^2\) and solve for V: \(V = 6000 \times (18.5)^2 = 2053500\).

Step 4 ：\(\boxed{\text{The value of a similar stone whose mass is 18.5 kg is Ksh 2,053,500}}\)