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  • Provide solution for RD Sharma maths class 12 chapter 12 Derivative as a Rate Measurer exercise multiple choise question 26

Provide solution for RD Sharma maths class 12 chapter 12 Derivative as a Rate Measurer exercise multiple choise question 26

Answers (1)

Answer:

\begin{aligned} &\text { A. } \frac{d h}{d t}=1 m / h r \end{aligned}

Hint:

The volume of a cylinder, of radius r and height h is defined as

\begin{aligned} &V(r, h)=\pi r^{2} h\\ \end{aligned}

Given:

\begin{aligned} &r=10 \mathrm{~m} \text { we get }\\ &V(h)=\pi \times 10^{2} \times h=100 \pi h \quad \quad \quad .....(i)\\ &\frac{d v}{d t}=314 m^{3} / h r \end{aligned}

Solution:

→ Differentiating (i) respect to t, we get

\begin{aligned} &\frac{d v}{d t}=100 \pi \frac{d h}{d t}\\ &\rightarrow \text { Substituting values and using } \quad \pi =\frac{3}{4} \text { we get } \end{aligned}

\begin{aligned} &314=100 \times 3.14 \frac{d h}{d t} \\ &\frac{d h}{d t}=1 \mathrm{~m} / \mathrm{hr} \end{aligned}

Posted by

Gurleen Kaur

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