Answer:
h = 9x
Step-by-step explanation:
Given: i. for the cylinder, base radius = 2x cm, height = h cm
ii. for the sphere, radius = 3x cm
iii. volume of the cylinder = volume of the sphere
volume of a cylinder is given as;
volume = 

h
where: r is its base radius and h the height
volume of the given cylinder = 
x
x h
= 
x 4
x h
= 

h
volume of a sphere = 


where r is the radius.
volume of the given sphere = 
x 
= 
x 9 
= 12

Since,
volume of the cylinder = volume of the sphere
Then we have;


h = 12

4
h = 36

subtract
from both sides
4
h = 36
x
divide both sides by 4
h = 
= 9x
h = 9x
Note that this a right-angled triangle with the right angle at Y.
<span>Use coordinates of the point to find XY and YZ </span>
<span>XY = 21 - (-3) </span>
<span>= 24 </span>
<span>YZ = 4 - (-6) </span>
<span>= 10 </span>
<span>Use Pythagoras theorem to XZ </span>
<span>XZ = sqrt[24^2 + 10^2] </span>
<span>= 26 </span>
<span>Perimeter = 26 + 24 + 10 </span>
<span>= 60</span>
According to above figure, the angles (8x - 20)° and (5x + 37)° are pairs of vertical opposite angles, so