CBSE (Science) Class 12CBSE
Share
Notifications

View all notifications

A Sphere of Radius 100 Mm Shrinks to Radius 98 Mm, Then the Approximate Decrease in Its Volume is - CBSE (Science) Class 12 - Mathematics

Login
Create free account


      Forgot password?

Question

A sphere of radius 100 mm shrinks to radius 98 mm, then the approximate decrease in its volume is

  • 12000 π mm3

  • 800 π mm3

  • 80000 π mm3

  • 120 π mm3

Solution

80000 π mm3
Let x be the radius of the sphere and y be its volume.

\[x = 100, x + ∆ x = 98\]

\[ \Rightarrow ∆ x = - 2\]

\[y = \frac{4}{3}\pi x^3 \]

\[ \Rightarrow \frac{dy}{dx} = 4\pi x^2 \]

\[ \Rightarrow \left( \frac{dy}{dx} \right)_{x = 100} = 40000\pi\]

\[ \therefore ∆ y = dy = \frac{dy}{dx}dx = 40000\pi \times \left( - 2 \right) = - 80000\pi\]

\[\text { Hence, the decrease in the volume of the sphere is } 80000\pi \text{mm}^ 3.\]

  Is there an error in this question or solution?

APPEARS IN

Video TutorialsVIEW ALL [2]

Solution A Sphere of Radius 100 Mm Shrinks to Radius 98 Mm, Then the Approximate Decrease in Its Volume is Concept: Approximations.
S
View in app×