Answer:
C. 128/3 meters cubed
Step-by-step explanation:
The volume of a cylinder is denoted by:  , where r is the radius and h is the height. We know it's equal to 64, so we can set that equal to V:
, where r is the radius and h is the height. We know it's equal to 64, so we can set that equal to V:


We know that the sphere and cylinder have the same height and radius. However, the "height" of a sphere is actually the same as its diameter, which is twice its radius. Then, we can replace h in the above equation with 2r:



Now, the volume of a sphere is denoted by:  , where r is the radius. From above, we know that
, where r is the radius. From above, we know that  , so we can plug this into the equation:
, so we can plug this into the equation:


Thus, the answer is C.
 
        
                    
             
        
        
        
Answer:
-¹²/₅  
Step-by-step explanation:
Let cos a = -⁵/₁₃
Then tan a = sin a/cos a
= [√(1 - cos²a)]/cos a
= {√[1 - (-⁵/₁₃)²]}/(-⁵/₁₃)
= -[√(1 - ²⁵/₁₆₉)] × ¹³/₅
= -[(√(¹⁴⁴/₁₆₉ )] × ¹³/₅
= -¹²/₁₃ × ¹³/₅
= -¹²/₅
tan(arccos (-⁵/₁₃)) = -¹²/₅
The diagram shows the 2nd  quadrant of a circle with radius 13, cos a = -⁵/₁₃, and tan a = ¹²/₍₋₅₎ = -¹²/₅.