1.2113 ft/s is the speed at which the radius of the sphere is changing when the radius is 6 feet .
Mensuration is a division of mathematics that studies geometric figure calculation and its parameters such as area, length, volume, lateral surface area, surface area, etc. It outlines the principles of calculation and discusses all the essential equations and properties of various geometric shapes and figures.
Mensuration is a subject of geometry. Mensuration deals with the size, region, and density of different forms both 2D and 3D. Now, in the introduction to Mensuration, let’s think about 2D and 3D forms and the distinction between them.
The rate of change of volume will be the product of the rate of change of radius and the area of the sphere. The area of the sphere is ...
A = 4πr² = 4π(6 ft)² = 144π ft²
Then the relationship above is ...
dV/dt = A·dr/dt
548 ft³/s = (144π ft²)·dr/dt
dr/dt = (548 ft³/s)/(144π ft²) = 137/(36π) ft/s ≈ 1.2113 ft/s
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