JEE Mains · Maths · STD 12 - 6. Application of derivatives
If the surface area of a cube is increasing at a rate of \(3.6 cm ^{2} / sec ,\) remaining its shape; then the rate of change of its volume (in \(cm ^{3} / sec\) ), when the length of a side of the cube is \(10 cm ,\) is
- A \(9\)
- B \(18\)
- C \(10\)
- D \(20\)
Answer & Solution
Correct Answer
(A) \(9\)
Step-by-step Solution
Detailed explanation
\(\frac{ d }{ dt }\left(6 a ^{2}\right)=3.6 \Rightarrow 12 a \frac{ da }{ dt }=3.6\) \(a \frac{ da }{ dt }=0.3\) \(\frac{ dv }{ dt }=\frac{ d }{ dt }\left( a ^{3}\right)=3 a \left( a \frac{ da }{ dt }\right)\) \(=3 \times 10 \times 0.3=9\)
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Maths
- Let \(y=y(x)\) be the solution of the differential equation \(\frac{d y}{d x}+3\left(\tan ^2 x\right) y+3 y=\sec ^2 x\)
\(y(0)=\frac{1}{3}+e^3\). Then \(y\left(\frac{\pi}{4}\right)\) is equal toJEE Mains 2025 Medium - The plane passing through the points \((1,2,1),(2,1,2)\) and parallel to the line, \(2 x=3 y, z=1\) also passes through the pointJEE Mains 2020 Hard
- Let \(f: R-\left\{\frac{\alpha}{6}\right\} \rightarrow R\) be defined by \(f(x)=\frac{5 x+3}{6 x-\alpha} .\) Then the value of \(\alpha\) for which \((fof)(x)=x\), for all \(x \in R-\left\{\frac{\alpha}{6}\right\}\), is:JEE Mains 2021 Medium
- The equation of line passing through \((-4, 1, 3)\), parallel to the plane \(x + 2y - z - 5 = 0\) and intersecting the line \(\frac{{x + 1}}{{ - 3}} = \frac{{y - 3}}{2} = \frac{{z - 2}}{{ - 1}}\) isJEE Mains 2019 Hard
- Let \(z\) be a complex number such that the real part of \(\frac{z-2 i}{z+2 i}\) is zero. Then, the maximum value of \(|\mathrm{z}-(6+8 \mathrm{i})|\) is equal to :JEE Mains 2024 Hard
- An ellipse has its center at (1,-2), one focus at (3,-2) and one vertex at \((5,-2)\). Then the length of its latus rectum is :JEE Mains 2026 Medium
More PYQs from JEE Mains
- Let \(A=\{1,2,3\}\). The number of relations on \(A\), containing \((1,2)\) and \((2,3)\), which are reflexive and transitive but not symmetric, is ______ -JEE Mains 2025 Easy
- Let \(A=\left[\begin{array}{lll}1 & 0 & 0 \\ 0 & \alpha & \beta \\ 0 & \beta & \alpha\end{array}\right]\) and \(|2 A|^3=2^{21}\) where \(\alpha, \beta \in Z\), Then a value of \(\alpha \) isJEE Mains 2024 Hard
- A hyperbola passes through the point \(P\left( {\sqrt 2 ,\sqrt 3 } \right)\) has foci at \(\left( { \pm 2,0} \right)\). Then the tangent to this hyperbola at \(P\) also passes through the pointJEE Mains 2017 Hard
- If the \(x\)-intercept of a focal chord of the parabola \(y^2=8 x+4 y+4\) is \(3\) , then the length of this chord is equal to \(.............\)JEE Mains 2023 Medium
- If the system of equations
\(x + 5y + 6z = 4\),
\(2x + 3y + 4z = 7\),
\(x + 6y + az = b\)
has infinitely many solutions, then the point \((a, b)\) lies on the lineJEE Mains 2026 Medium - Consider the function \(f:(0, \infty) \rightarrow R\) defined by \(f(x)=e^{-\left|\log _e x\right|}\). If \(m\) and \(n\) be respectively the number of points at which \(f\) is not continuous and \(f\) is not differentiable, then \(\mathrm{m}+\mathrm{n}\) isJEE Mains 2024 Hard