TS EAMCET · Maths · Application of Derivatives
The radius of a sphere is changing. At an instant of time the rate of change in its volume and its surface area are equal. Then the value of radius at that instant is?
- A 1
- B 2
- C \(\frac{3}{2}\)
- D 3
Answer & Solution
Correct Answer
(B) 2
Step-by-step Solution
Detailed explanation
Given that, at any instant of time Rate of change in volume w.r.t. time \(=\) rate of change in surface area w.r.t. time i.e., \(\frac{d v}{d t}=\frac{d s}{d t}\) \(\ldots(i)\) Volume of sphere of radius \((r), V=\frac{4}{3} \pi r^3\) Differentiating w.r.t, ' \(t\) ', we get…
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
- \(\lim _{x \rightarrow-2^{+}}\left([x]^2-[x]-2\right)+\lim _{x \rightarrow-3^{-}}\left([x]^2-4[x]+3\right)=\)TS EAMCET 2023 Easy
- In a test, a student either guesses or copies or knows the answer to a multiple choice question with four choices having one correct answer. The probability that he guesses the answer is \(\frac{1}{3}\) and the probability that he copies it is \(\frac{1}{12}\). The probability that his answer is correct given that he copied it is \(\frac{1}{6}\). The probability that he knew the answer, given that he has correctly answered it, isTS EAMCET 2018 Hard
- \((1, k)\) is a point on the circle passing through the points \((-1,1),(0,-1)\) and \((1,0)\). If \(k \neq 0\), then \(k=\)TS EAMCET 2024 Easy
- If the integer represented by 100 ! has \(K\) consective zeroes at the end, then \(K=\)TS EAMCET 2018 Medium
- If and thenTS EAMCET 2022 Medium
- If \(f(x)=\tan ^{-1}\left(\frac{1}{\sin ^2 x+\sin x+1}\right)\) \(+\tan ^{-1}\left(\frac{1}{\sin ^2 x+3 \sin x+3}\right)+\tan ^{-1}\) \(\left(\frac{1}{\sin ^2 x+5 \sin x+7}\right)+\ldots+\) upto 10 terms
then \(f^{\prime}(0)=\)TS EAMCET 2020 Hard
More PYQs from TS EAMCET
- \(\alpha, \beta, \gamma\) are the roots of the equation \(x^3-10 x^2+7 x+8=0\). Match the following and choose the correct answer.
TS EAMCET 2004 Hard - A particle having kinetic energy \(K\) is projected at \(60^{\circ}\) with the horizontal. The kinetic energy at the highest point isTS EAMCET 2020 Medium
- A carrier wave of peak voltage is used to transmit a message signal. What should be the peak voltage of the modulating signal in order to have a modulation index ofTS EAMCET 2021 Easy
- A transverse wave propagating on a stretched string of linear density \(3 \times 10^{-4} \mathrm{~kg} \mathrm{~m}^{-1}\) is represented by the equation \(y=0.2 \sin (15 x+60 t)\) where \(x\) is in metres and \(t\) is in seconds. The tension in the string (in newton) isTS EAMCET 2005 Hard
- If the mean and variance of a Binomial variable \(X\) are \(\frac{5}{2}\) and \(\frac{5}{4}\) respectively, then \(P(X>1)=\)TS EAMCET 2018 Easy
- Which one of the following is not an example of condensation polymer?TS EAMCET 2024 Easy