Find the rate of change of the volume of a cube when the side of the cube is 10 cm , given that the side is changing at a rate of 4 cm/s . - Mathematics MCQ Mathematics Mock Test - 1 2026 | ExamTest.live

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Find the rate of change of the volume of a cube when the side of the cube is 10 cm, given that the side is changing at a rate of 4 cm/s .

Solution & Step-by-step Explanation

Let L be the side of the cube and V be its volume.Given L = 10 cm and \frac{d L}{d t} = 4 cm/s .The volume of a cube is V = L^{3} .Differentiating with respect to time t : \frac{d V}{d t} = \frac{d}{d t} (L^{3}) = 3 L^{2} \cdot \frac{d L}{d t} Substitute the given values: \frac{d V}{d t} = 3 (10)^{2} \cdot 4 \frac{d V}{d t} = 3 (100) \cdot 4 = 1200 cm^{3} /s

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Find the rate of change of the volume of a cube when the side of the cube is 10 cm, given that the side is changing at a rate of 4 cm/s .

800 cm^{3} /s

1000 cm^{3} /s

1200 cm^{3} /s

500 cm^{3} /s

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