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  • Need solution for RD Sharma maths class 12 chapter 12 Derivative as a Rate Measurer exercise multiple choise question 11

Need solution for RD Sharma maths class 12 chapter 12 Derivative as a Rate Measurer exercise multiple choise question 11

Answers (1)

Answer:

B.\; \; 180\pi \; \; cm^{3}/min

Hint:

Here we use formula of a sphere of radius r is defined by

\begin{aligned} &V(r)=\frac{4}{3} \pi r^{3} \quad \quad \quad \quad....(i) \end{aligned}

Given:

\begin{aligned} &r=15 \mathrm{~cm} \; \; \; \frac{d r}{d t}=0.2 \mathrm{~cm} / \mathrm{min} \end{aligned}

Solution:

→ Differentiating (i) with respect to t, we get

\begin{aligned} &\frac{d V}{d t}=4 \pi r^{2} \times \frac{d r}{d t} \\ &\frac{d V}{d t}=4 \pi \times 15^{2} \times 0.2=180 \pi \mathrm{cm}^{3} / \mathrm{min} \end{aligned}

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Gurleen Kaur

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