TS EAMCET · Maths · Application of Derivatives
The height (in cm) of a cylinder of the greatest volume that can be inscribed in a sphere of radius , is
- A
- B
- C
- D
Answer & Solution
Correct Answer
(B)
Step-by-step Solution
Detailed explanation
∴R2=r2+h22 r2=R2-h22 Given, radius of sphere R=3 cm Volume of cylinder =πr2h =πR2-h22h dvdh=πR2-h24+-2h24 dvdh=0 ∴πR2-h24-2h24=0 R2-3h24=0 R2=3h24 h=2R3=2×33=23 cm In neighbourhood of h=23 cm, dvdh is changing sign from…
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
- \(\lim _{x \rightarrow 0} \frac{\left(3^{2 x}-\sqrt{x+1}\right) \sin 5 x}{1-\cos 4 x}=\)TS EAMCET 2023 Easy
- If \(a x^2+b y^2=15\) is the equation of the ellipse for which distance between its foci is 2 and distance between its directrices is 5 , then \(a+b=\)TS EAMCET 2022 Hard
- If and are the roots of the equation where are rational numbers, then the roots of the equation areTS EAMCET 2022 Easy
- If sum of the coefficients of \(x^r(r=0,1,2, \ldots, 2 n)\) in the expansion of \(\left(1+3 x-2 x^2\right)^n\) is 128 , then \(\sum_{r=1}^{2 n} r \frac{(2 n)_{C_r}}{(2 n)_{C_{r-1}}}=\)TS EAMCET 2020 Hard
- The area of the region bounded by the curves \(y=x^3, y=x^2\) and the lines \(x=0\) and \(x=2\) isTS EAMCET 2025 Medium
- \[ \lim _{x \rightarrow 0} \frac{4[\sin (2022 x)-\sin (2020 x)]}{x[\cos (2022 x)+2 \cos (2021 x)+\cos (2020 x)]}= \]TS EAMCET 2022 Medium
More PYQs from TS EAMCET
- A \(4 \mu \mathrm{F}\) capacitor is charged by a \(200 \mathrm{~V}\) battery. It is then disconnected from the supply and is connected to another uncharged \(2 \mu \mathrm{F}\) capacitor. During the process, loss of energy (in \(\mathrm{J}\) ) isTS EAMCET 2005 Medium
- If \(x\) and \(y\) are real numbers such that, \(\hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}},-2 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}+2 \hat{\mathbf{k}}, x \hat{\mathbf{i}}-5 \hat{\mathbf{j}}+3 \hat{\mathbf{k}}\), \(\hat{\mathbf{i}}+y \hat{\mathbf{j}}-\hat{\mathbf{k}}\) are the position vectors of four coplanar points, then the locus of \(P(x, y)\) isTS EAMCET 2021 Easy
- A parallel plate capacitor of capacity \(C_0\) is charged to a potential \(V_0\). (i) The energy stored in the capacitor when the battery is disconnected and the plate separation is doubled is \(E_1\). (ii) The energy stored in the capacitor when the charging battery is kept connected and the separation between the capacitor plates is doubled is \(E_2\). Then, \(E_1 / E_2\) value is:TS EAMCET 2003 Medium
- A segment of wire vibrates with a fundamental frequency of \(450 \mathrm{~Hz}\) under a tension of \(9 \mathrm{~kg} \mathrm{wt}\). Then tension at which the fundamental frequency of the same wire becomes \(900 \mathrm{~Hz}\) isTS EAMCET 2007 Easy
- For what values of ' \(a\) ', the system of equations \(x+y+z=12 x+3 y+2 z=2\), \(a x+a y+2 a z=4\) will have a unique solution?TS EAMCET 2019 Easy
- oxidises oxalic acid in acidic medium. The number of molecules produced per mole of isTS EAMCET 2021 Hard