Download App

Application of Derivatives — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSApplication of Derivatives3 Marks
Question
A balloon, which always remains spherical has a variable radius. Find the rate at which its volume is increasing with the radius when the later is $10 \ cm.$
✓

Answer

Since, $V = \frac{4}{3}\pi {x^3}$
$\therefore \frac{{dV}}{{dx}} = \frac{d}{{dt}}\left( {\frac{4}{3}\pi {r^3}} \right)$
$= \frac{4}{3}\pi .3{r^2} = 4\pi {r^2}$
At $x = 10 \ cm$
$\Rightarrow \frac{{dV}}{{dx}} = 4\pi {\left( {10} \right)^2} = 400\pi $
Therefore, the volume is increasing at the rate of $400\pi \ cm^3/\sec.$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "3 Marks Question" from Application of Derivatives→Application of Derivatives — all question types→MATHS STD 12 Science question papers→Rajasthan Board STD 12 Science question papers→Rajasthan Board question paper generator→

Similar questions

The money to be spent for the welfare of the employees of a firm is proportional to the rate of change of its total revenue $($Marginal revenue$).$ If the total revenue $($in rupees$)$ recieved from the sale of $x$ units of a product is given by $R(x) = 3x^2 + 36x + 5,$ find the marginal revenue, when $x = 5,$ and write which value does the question indicate.
→
Let $f : R \rightarrow R$ be the function defined by $f(x) = 4x - 3$ for all $x \in R.$ Then write $f^{-1}.$
→
Find the coordinates of the point where the line through (3, -4, -5) and (2, -3, 1) corsses the plane 2x + y + z = 7.
→
Evaluate the following integrals:
$\int\text{e}^{\text{x}}(\cot\text{x}+\log\sin\text{x})\text{dx}$
→
Three cards are drawn successively with replacement from a well shuffled pack of 52 cards. Find the probability distribution of the number of spades. Hence, find the mean of the distribution.
→
Find the coordinates of the foot of the perpendicular drawn from the origin. $3y + 4z - 6 = 0$
→
For each of the differential equations given in find the general solution:$\text{y dx}+(\text{x}-\text{y}^{2})\ \text{dy}=0$
→
Show that the relation R in R defined as R = {(a, b) : a $\leq$ b}, is reflexive and transitive but not symmetric.
→
Evaluate the following:
$\int\frac{\text{e}^{6\log\text{x}}-\text{e}^{5\log\text{x}}}{\text{e}^{4\log\text{x}}-\text{e}^{3\log\text{x}}}\text{dx}$
→
Evaluate the following integrals:
$\int(\text{a}\tan\text{x}+\text{b}\cot \text{x})^2\text{dx}$
→