The radius of a sphere shrinks from 10 to 9.8cm. Find approximate… - Vidyadip

Question

The radius of a sphere shrinks from 10 to 9.8cm. Find approximately the decrease in its volume.

✓

Answer

Let $\text{x}=10,\\\text{x}+\triangle\text{x}=9.8$
$\triangle\text{x}=9.8-\text{x}$
$=9.8-10$
$\triangle\text{x}=-0.2$
$\text{y}=\frac{4}{3}\pi\text{x}^3$
$\frac{\text{dy}}{\text{dx}}=4\pi\text{r}^2$
$\Big(\frac{\text{dy}}{\text{dx}}\Big)_{\text{x}\Rightarrow10}=4\pi(10)^2$
$\Big(\frac{\text{dy}}{\text{dx}}\Big)_{\text{x}\Rightarrow10}=400\pi\ \text{cm}^2$
$=400\pi\times(-0.2)$
$\triangle\text{y}=-80\pi\ \text{cm}^3$
so, approximate decrease in volume is $80\pi\ \text{cm}^3$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "5 Marks Questions" from Differentials, Errors and Approximations→Differentials, Errors and Approximations — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

Show that the points whose position vectors are as given below are collinear:
$2\hat{\text{i}}+\hat{\text{j}}-\hat{\text{k}},\ 3\hat{\text{i}}-2\hat{\text{j}}+\hat{\text{k}}$ and $\hat{\text{i}}+4\hat{\text{j}}-3\hat{\text{k}}$

Find the points of discontinuity, if any of the following function:
$\text{f(x)}=\begin{cases}\sin\text{x}-\cos\text{x},&\text{if }\text{ x}\neq0\\-1,&\text{if }\text{ x}=0\end{cases}$

Assume that a rain drop evaporates at a rate proportional to its surface area. Form a differential equation involving the rate of change of the radius of the rain drop.

If $\text{y}=\sin^{-1}\big(6\text{x}\sqrt{1-9\text{x}^2}\big), -\frac{1}{3\sqrt{2}}<\text{x}<\frac{1}{3\sqrt{2}},$ then find $\frac{\text{dy}}{\text{dx}}.$

For the matrix $\text{A}=\begin{bmatrix}1&1&1\\1&2&-3\\2&-1&3\end{bmatrix}$Show that $A^3 - 6A^2 + 5A + 11I = 0$. Hence, find $A^{-1}.$

A manufacturing company makes two types of teaching aids A and B of Mathematics for class XII. Each type of A requires 9 labour hours of fabricating and 1 labour hour for finishing. Each type of B requires 12 labour hours for fabricating and 3 labour hours for finishing. For fabricating and finishing, the maximum labour hours available per week are 180 and 30 respectively. The company makes a profit of A and ₹ 80 on each piece of type ₹ 120 on each piece of type B. How many pieces of type A and type B should be manufactured per week to get a maximum profit? Make it as an LPP and solve graphically. What is the maximum profit per week?

A manufacturing company makes two models A and B of a product. Each piece of model A requires 9 labour hours for fabricating and 1 labour hour for finishing. Each piece of model B requires 12 labour hours for fabricating and 3 labour hours for finishing. For fabricating and finishing, the maximum labour hours available are 180 and 30 respectively. The company makes a profit of Rs. 8000 on each piece of model A and Rs. 12000 on each piece of model B. How many pieces of model A and model B should be manufactured per week to realise a maximum profit? What is the maximum profit per week?

Solve the following differential equation :
$
\left(x^3+x^2+x+1\right) \frac{d y}{d x}=2 x^2+x
$

$=\begin{bmatrix}1&1&\text{x}\end{bmatrix}\begin{bmatrix}1&0&2\\0&2&1\\2&1&0\end{bmatrix}\begin{bmatrix}1\\1\\1\end{bmatrix}=0,$ find x.

Prove that:
$\cos^{-1}\frac{4}{5}+\cos^{-1}\frac{12}{13}=\cos^{-1}\frac{33}{65}$