Question

A Test tube has lower part as hemisphere and upper part is cylindrical with same radius. If
6 cm water is added to the test-tube, it will be just completely filled , but if, cm' water
is added, 5 cm height will remain empty. Calculate the radius of the test-tube and the height of
the cylindrical part. (n = 2)​

Answer 1

Radius = 6.3 cm

Height = 2.54 cm

Step-by-step explanation:

Total volume = Volume of cylinder + volume of the hemisphere

= πr^2h + 2/3*πr^3

Given total volume is 5159 / 6 cu. cm.

So 5159 / 6 = πr^2h + 2/3*πr^3 = πr^2 ( h + 2/3r) ---------------------- (1)

Given 2002/ 3 cu.cm =  πr^2(h-5) + 2/3*πr^3

2002/ 3 = πr^2h − 5πr^2 + 2/3*πr^3

2002/ 3 = πr^2 (h - 5 + 2/3r) -------------------------------(2)

 

​Solving equations 1 & 2, we get:

r = 6.3 cm

h = 2.54 cm