Question

given that V= πr2 h + 2/3 πr3
(i) make h the subject of the formula
(ii) find the value of h when V = 245 and r= 7.​

Answer 1

Answer:

(i)

$h = \frac{v - \frac{2}{3}\pi {r}^{3} }{\pi {r}^{2} }$

(ii)

$h = - 3.76$

Step-by-step explanation:

(I) Make h the subject of the formula:

Given:

$v = \pi {r}^{2} h + \frac{2}{3} \pi {r}^{3}$

Step 1:

$v - \frac{2}{3} \pi {r}^{3} = \pi r^{2} h$

Step 2:

$\frac{v - \frac{2}{3}\pi {r}^{3} }{\pi {r}^{2} } = h$

or

$h = \frac{v - \frac{2}{3}\pi {r}^{3} }{\pi {r}^{2} }$

(ii) Find the value of h when V = 245 and r = 7:

We put values of V and r in above derived formula.

π= 22/7

$h = \frac{245- \frac{2}{3}( \frac{22}{7} ) {(7)}^{3} }{( \frac{22}{7} ) {(7)}^{2} } \\ h = \frac{245- \frac{2}{3}( 22) {(7)}^{2} }{( 22 ) {(7)}}$

After solving this, we get final value of h as:

$h = - 3.76$