Q82.If a right circular cone, having maximum volume, is inscribed in a sphere of radius 3 cm, then the curved surface area (in cm2 ) of this cone is : (1) 8√2π (2) 6√2π (3) 8√3π (4) 6√3π
What This Question Tests
This question involves setting up an optimization problem by relating the dimensions of an inscribed cone to the sphere's radius, finding the maximum volume using differentiation, and then calculating the curved surface area.
Concepts Tested
Formulas Used
Volume of cone V = (1/3)πr^2h
Curved surface area of cone CSA = πrl
Relationship between r, h, and R (sphere radius): r^2 = R^2 - (h-R)^2
First derivative test for maxima/minima
📚 NCERT Sections This Tests
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9.5 A small bulb is placed at the bottom of a tank containing water to a depth of 80cm. What is the area of the surface of water through which light from the bulb can emerge out? Refractive index of water is 1.33. (Consider the bulb to be a point source.)
9.1 — A Small Candle, 2.5 Cm In Size Is Placed At 27 Cm In Front Of A Concave
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9.1 A small candle, 2.5 cm in size is placed at 27 cm in front of a concave mirror of radius of curvature 36 cm. At what distance from the mirror should a screen be placed in order to obtain a sharp image? Describe the nature and size of the image. If the candle is moved closer to the mirror, how would the screen have to be moved?
2.4 — A Spherical Conductor Of Radius 12 Cm Has A Charge Of 1.6 × 10–7C
Physics Class 11 · Chapter 2
2.4 A spherical conductor of radius 12 cm has a charge of 1.6 × 10–7C distributed uniformly on its surface. What is the electric field (a) inside the sphere (b) just outside the sphere (c) at a point 18 cm from the centre of the sphere?
📋 Question Details
- Chapter
- Applications of Derivatives
- Topic
- Optimization
- Year
- 2018
- Shift
- 15 Apr
- Q Number
- Q82
- Type
- MCQ
- NCERT Ref
- Class 12 Mathematics Ch 6: Applications of Derivatives
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