JEE Mains · Maths · STD 12 - 6. Application of derivatives
If a right circularcone having maximum volume, is inscribed in a sphere of radius \(3\, cm\), then the curved surface area (in \(cm^2\)) of this cone is
- A \(8\sqrt 3 \pi \)
- B \(6\sqrt 2 \pi \)
- C \(6\sqrt 3 \pi \)
- D \(8\sqrt 2 \pi \)
Answer & Solution
Correct Answer
(A) \(8\sqrt 3 \pi \)
Step-by-step Solution
Detailed explanation
Sphere of radius \(r=3 \mathrm{cm}\) Let \(b, h\) be base radius and height of cone respectively. So, volume of \(\mathrm{cone}=\frac{1}{2} \pi b^{2} h\) In right angled \(\Delta A B C\) by Pythagoras theorem \((h-r)^{2}+b^{2}=r^{2}\)…
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, \(x\frac{{dy}}{{dx}} + y = x\,{\log _e}\,x,\,\left( {x > 1} \right)\) If \(2y(2) = log_e\, 4 -1\), then \(y(e)\) is equal toJEE Mains 2019 Hard
- Let \(d\) be the distance of the point of intersection of the lines \(\frac{x+6}{3}=\frac{y}{2}=\frac{z+1}{1} \quad\) and \(\frac{x-7}{4}=\frac{y-9}{3}=\frac{z-4}{2}\) from the point \((7,8,9)\). Then \(\mathrm{d}^2+6\) is equal to :JEE Mains 2024 Medium
- Let \(3,6,9,12, \ldots\) upto \(78\) terms and \(5,9,13,17, \ldots\) upto \(59\) terms be two series. Then, the sum of the terms common to both the series is equal toJEE Mains 2022 Easy
- When a missile is fired from a ship, the probability that it is intercepted is \(\frac{1}{3}\) and the probability that the missile hits the target, given that it is not intercepted, is \(\frac{3}{4}\). If three missiles are fired independently from the ship, then the probability that all three hit the target, isJEE Mains 2021 Easy
- Let \(x_{0}\) be the point of local maxima of \(f(x)=\vec{a} \cdot(\vec{b} \times \vec{c}),\) where \(\vec{a}=x \hat{i}-2 \hat{j}+3 \hat{k}\) \(\overrightarrow{ b }=-2 \hat{ i }+ x \hat{ j }-\hat{ k }\) and \(\overrightarrow{ c }=7 \hat{ i }-2 \hat{ j }+ x \hat{ k } \cdot\) Then the value of \(\vec{a} \cdot \vec{b}+\vec{b} \cdot \vec{c}+\vec{c} \cdot \vec{a}\) at \(x=x_{0}\) isJEE Mains 2020 Hard
- Let the circle \(C_1: x^2+y^2-2(x+y)+1=0\) and \(C_2\) be a circle having centre at \((-1,0)\) and radius \(2\) . If the line of the common chord of \(\mathrm{C}_1\) and \(\mathrm{C}_2\) intersects the \(\mathrm{y}\)-axis at the point \(\mathrm{P}\), then the square of the distance of \(\mathrm{P}\) from the centre of \(\mathrm{C}_1\) is :JEE Mains 2024 Hard
More PYQs from JEE Mains
- Let \(\alpha_1, \alpha_2, \ldots, \alpha_7\) be the roots of the equation \(x^7+\) \(3 x^5-13 x^3-15 x=0\) and \(\left|\alpha_1\right| \geq\left|\alpha_2\right| \geq \ldots \geq\left|\alpha_7\right|\). Then \(\alpha_1 \alpha_2-\alpha_3 \alpha_4+\alpha_5 \alpha_6\) is equal to \(..................\).JEE Mains 2023 Hard
- The number of elements in the set \(S=\left\{x \in R : 2 \cos \left(\frac{x^{2}+x}{6}\right)=4^{x}+4^{-x}\right\}\) is\(.....\)JEE Mains 2022 Medium
- When a certain biased die is rolled, a particular face occurs with probability \(\frac{1}{6}-\mathrm{x}\) and its opposite face occurs with probability \(\frac{1}{6}+\mathrm{x}\). All other faces occur with probability \(\frac{1}{6}\). Note that opposite faces sum to \(7\) in any die. If \(0\,<\,x\,<\,\frac{1}{6}\), and the probability of obtaining total \(\mathrm{sum}=7\), when such a die is rolled twice, is \(\frac{13}{96}\), then the value of \(x\) is:JEE Mains 2021 Hard
- Let the function \(f(x)=\left(x^2+1\right)\left|x^2-a x+2\right|+\cos |x|\) be not differentiable at the two points \(x=\alpha=2\) and \(x=\beta\). Then the distance of the point \((\alpha, \beta)\) from the line \(12 x+5 y+10=0\) is equal to :JEE Mains 2025 Hard
- Let \(\alpha \) and \(\beta \) be the roots of the quadratic equation \({x^2}\,\sin \,\theta - x\,\left( {\sin \,\theta \cos \,\,\theta + 1} \right) + \cos \,\theta = 0\,\left( {0 < \theta < {{45}^o}} \right)\) , and \(\alpha < \beta \). Then \(\sum\limits_{n = 0}^\infty {\left( {{\alpha ^n} + \frac{{{{\left( { - 1} \right)}^n}}}{{{\beta ^n}}}} \right)} \) is equal toJEE Mains 2019 Hard
- Let \( S=\frac{1}{25!}+\frac{1}{3!23!}+\frac{1}{5!21!}+. \dots \) up to 13 terms. If \( 13S=\frac{2^{k}}{n!} \) where \( k\in N \), then \( n+k \) is equal toJEE Mains 2026 Easy