Q87.A water tank has the shape of a right circular cone with axis vertical and vertex downwards. Its semivertical angle is tan−1 34 . Water is poured in it at a constant rate of 6 cubic meter per hour. The rate (in square meter per hour), at which the wet curved surface area of the tank is increasing, when the depth of water in the tank is 4 meters, is _______.
What This Question Tests
This problem involves related rates, requiring the student to relate the volume of water, its depth, and the wet surface area using trigonometric properties of a cone, and then differentiate with respect to time.
Concepts Tested
Formulas Used
V = (1/3)πr²h
A = πr√(r²+h²)
r = h tanθ
📚 NCERT Sections This Tests
9.5 — A Small Bulb Is Placed At The Bottom Of A Tank Containing Water To A
Physics Class 12 · Chapter 9
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.)
9.3 — A Tank Is Filled With Water To A Height Of 12.5 Cm. The Apparent
Physics Class 12 · Chapter 9
9.3 A tank is filled with water to a height of 12.5 cm. The apparent depth of a needle lying at the bottom of the tank is measured by a microscope to be 9.4 cm. What is the refractive index of water? If water is replaced by a liquid of refractive index 1.63 up to the same height, by what distance would the microscope have to be moved to focus on the needle again?
8.1 — Figure 8.5 Shows A Capacitor Made Of Two Circular Plates Each Of
Physics Class 11 · Chapter 8
8.1 Figure 8.5 shows a capacitor made of two circular plates each of radius 12 cm, and separated by 5.0 cm. The capacitor is being charged by an external source (not shown in the figure). The charging current is constant and equal to 0.15A. (a) Calculate the capacitance and the rate of change of potential difference between the plates. (b) Obtain the displacement current across the plates. (c) Is Kirchhoff’s first rule (junction rule) valid at each plate of the capacitor? Explain. FIGURE 8.5
📋 Question Details
- Chapter
- Applications of Derivatives
- Topic
- Rate of Change
- Year
- 2022
- Shift
- 27 Jul Shift 2
- Q Number
- Q87
- Type
- Numerical
- NCERT Ref
- Class 12 Mathematics Ch 6: Applications of Derivatives
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