Maths-
General
Easy
Question
The radius and height of a cylinder are equal to the radius of sphere The ratio of the rates of change of the volume of the sphere and cylinder is
- 4:3
- 3:4
- 2:3
- 3:2
Hint:
The area of mathematics that deals with continuous change is calculus. Calculus is also known as "the calculus of infinitesimals" or "infinitesimal calculus." The study of continuous change in functions is the purpose of classical calculus. Here we have to find the ratio of the rates of change of the volume of the sphere and cylinder.
The correct answer is: 4:3
The three-dimensional shape of a cylinder is made up of two parallel circular bases connected by a curved surface. The right cylinder is created when the centres of the circular bases cross each other. The axis, which represents the height of the cylinder, is the line segment that connects the two centres.
A geometric shape with a sphere-like appearance. In three dimensions, the sphere is defined. The sphere is a three-dimensional solid with a volume and surface area. Each point of the sphere is equally spaced from the centre, much like a circle.
Now we have given: The radius and height of a cylinder are equal to the radius of sphere.
Here we used the concept of differentiation and the formulas of cylinder and sphere to find the ratio. Given that the ratio of the rates of growth of the sphere's and cylinder's volumes is 3:4, the ratio of the rates of growth of the cylinder's volume to that of the sphere's volume is 4:3.
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