Question

A cylinder has a volume of 200 mm3 and a height of 17 mm.

a) The volume formula for a cylinder is v = pie r squareℎ. Isolate for the variable r in this formula.

b) Using the equation where you isolated for r in part a, find the radius of the cylinder. Round your answer to the nearest hundredth. (1 mark)​

Answer 1

The radius of the cylinder is 1.93mm.

Explanation:

1) Formula to find the missing radius : V= pi r^2 (h)

( V= volume, pi=3.14 r=radius, h= height)

2) Plug all the give variables into the formula: 200=pi r^2 (17)

3) Multiply pi with 17 and then round it to the nearest hundredth which you get 53.401707511 -> 53.41, now your equation is: 200= 53.41 r^2

4) Next you want to isolate the r^2 by dividing both sides by 53.41

200/53.41= 53.41r^2/53.41 ( 3.74461711 round to the nearest hundredth --> 3.74) ---> 3.74=r^2

5) Now you have to square both sides to get rid of that exponent : squared 3.74 = squared r^2

6) Your equation would be 1.933907961 = r, round that whole decimal to the nearest hundredth and you will get 1.93 ( 19.3 = r)

7) So the radius of the cylinder given the volume is 200 mm^3 and a height of 17 mm is 1.93 mm.