Share

Books Shortlist

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

#### 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?

#### 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