Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
BITSAT 2021
Exam
BITSAT
Year
2021
Subject
Mathematics
Chapter
Application of Derivatives

BITSAT 2021 · Mathematics · Application of Derivatives

If the radius of a sphere is measured as 9 cm with an error of 0.03...

If the radius of a sphere is measured as 9cm9 \mathrm{ cm} with an error of 0.03cm0.03 \mathrm{ cm}, then find the approximating error in calculating its volume.

Options

  1. A2.46πcm32.46 \pi \mathrm{cm}^{3}
  2. B8.62πcm38.62 \pi \mathrm{cm}^{3}
  3. C9.72πcm39.72 \pi \mathrm{cm}^{3}
  4. D7.6πcm37.6 \pi \mathrm{cm}^{3}

Correct answer

C. 9.72πcm39.72 \pi \mathrm{cm}^{3}

Step-by-step solution

Let rr be the radius of the sphere and Δr\Delta r be the error in measuring the radius. Then, r=9cmr=9 \mathrm{ cm} and Δr=0.03cm\Delta r=0.03 \mathrm{ cm} Let VV be the volume of the sphere. Then, V=43πr3⇒dVdr=4πr2⇒(dVdr)r=9=4π×92=324π\begin{array}{l} \mathrm{V}=\frac{4}{3} \pi r^{3} \\ \Rightarrow \frac{\mathrm{dV}}{\mathrm{dr}}=4 \pi r^{2} \\ \Rightarrow\left(\frac{\mathrm{dV}}{\mathrm{dr}}\right)_{r=9}=4 \pi \times 9^{2}=324 \pi \end{array}Let \Delta \mathrm{V} be the error in \mathrm{V}duetoerrorΔdue to error \Delta\mathrm{r}inin r.Then,. Then,ΔV=dVdrΔr⇒ΔV=324π×0.03=9.72πcm3\begin{array}{l}\Delta \mathrm{V}=\frac{\mathrm{dV}}{\mathrm{dr}} \Delta r \\ \Rightarrow \Delta \mathrm{V}= 324 \pi \times0.03=9.72 \pi \mathrm{cm}^{3} \end{array}$
Practice Application of Derivatives on Quantrex Academy →

More from Application of Derivatives

The maximum area of rectangle inscribed in a circle of diameter R is BITSAT 2024Consider the function f(x)=(|x-1|)/(x^2) , then f(x) is BITSAT 2024The maximum volume (in cu. units) of the cylinder which can be inscribed in a sphere of… BITSAT 2024If the angle made by the tangent at the point (x_0, y_0) on the curve x=12(t+ t t)… BITSAT 2024The altitude of a cone is 20 cm and its semivertical angle is 30^ ^ ∘ . If the… BITSAT 2024The point of inflexion for the curve y=(x-a)^n , where n is odd integer and n ≥ 3 is BITSAT 2024The population p(t) at time t of a certain mouse species satisfies the differential… BITSAT 2024The function f(x)= (1+x)-(2 x)/(2+x) is increasing on BITSAT 2023If f(x)= x, g(x)= 2 x, h(x)= 3 x and I(x)= x , then which of the following option is… BITSAT 2023The interval in which the function f(x)=(4 x^2+1)/(x) is decreasing is : BITSAT 2023The curve given by x+y=e^ x y has a tangent parallel to the Y-axis at the point BITSAT 2023The function f(x)= ^ -1 ( x+ x) is an increasing function in BITSAT 2023A running track of 440 ft is to be laid out enclosing a football field, the shape of… BITSAT 2022A spherical balloon is filled with 4500 π cubic meters of helium gas. If a leak in the… BITSAT 2022The points at which the tangent passes through the origin for the curve y=4 x^ 3 -2 x^ 5… BITSAT 2021f(x)= ( e^ 2 x -1 e^ 2 x +1 )is BITSAT 2021 Full Application of Derivatives list Application of Derivatives JEE Maths PYQsJEE Mathematics PYQs All BITSAT PYQs