Moderate -0.5 This is a straightforward connected rates of change problem requiring the chain rule: V = x³, so dV/dt = 3x²(dx/dt). With given values dx/dt = 0.01 and x = 20, it's direct substitution into a standard formula. Slightly easier than average as it's a single-step application with no geometric complications or algebraic manipulation required.
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\includegraphics[max width=\textwidth, alt={}, center]{5e3e5418-7976-4232-8550-1da6420a3fcb-05_424_529_248_815}
The diagram shows a cubical closed container made of a thin elastic material which is filled with water and frozen. During the freezing process the length, \(x \mathrm {~cm}\), of each edge of the container increases at the constant rate of 0.01 cm per minute. The volume of the container at time \(t\) minutes is \(V \mathrm {~cm} ^ { 3 }\).
Find the rate of increase of \(V\) when \(x = 20\).
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\includegraphics[max width=\textwidth, alt={}, center]{5e3e5418-7976-4232-8550-1da6420a3fcb-05_424_529_248_815}
The diagram shows a cubical closed container made of a thin elastic material which is filled with water and frozen. During the freezing process the length, $x \mathrm {~cm}$, of each edge of the container increases at the constant rate of 0.01 cm per minute. The volume of the container at time $t$ minutes is $V \mathrm {~cm} ^ { 3 }$.
Find the rate of increase of $V$ when $x = 20$.\\
\hfill \mbox{\textit{CAIE P1 2023 Q3 [3]}}