A sphere is a perfectly round three-dimensional geometric shape where every point on its surface is equidistant from its center. Defined by its radius it has no edges or vertices. Spheres are widely used in physics and engineering and geometry to model objects like planets and balls and calculate surface area and volume.
Class 12 Maths Chapter 6 focuses on Applications of Derivatives for CBSE Exam 2024-25. It includes rate of change of quantities increasing and decreasing functions tangents and normals maxima and minima. These concepts are applied to solve problems in physics economics and engineering while improving analytical skills and understanding of mathematical applications in various fields.
The correct answer is: surface area times the rate of change of radius.
This follows because the volume V of a sphere is connected to its radius r by the formula:
V = (4/3) π r³
The rate of change of volume with respect to time is:
dV/dt = 4 π r² (dr/dt)
Here, 4 π r² is the surface area of the sphere, and (dr/dt) is the rate of change of the radius. Therefore, the rate of change of volume is equal to the surface area times the rate of change of radius.
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