What is the volume of cylinder B?

Question

The volume of a cylinder varies jointly with the square or its radius and with its height: V=kr^2h

 

Cylinder A has a volume of 254.34 cubic inches and has a radius of 3 inches and a height of 9 inches. What is the volume of cylinder B, which has a radius of 4 inches and a height of 5 inches?

Answer 1

Given V = k * r² * h

 

Given V_A = 254.34 in³, r_A = 3 in and h_A = 9 in

 

Also, r_B = 4 in and h_B = 5 in.

 

k = V_A/(r_A² * h_A) = V_B/(r_B² * h_B)

 

=> V_B = (r_B/r_A)² * (h_B/h_A) * V_A

 

          = (4/3)² * (5/9) * 254.34

 

          = (80/81) * 254.34 = 251.2 in³

 

 

Answer 2

Given that, V=kr²h ..................(1)

=>k=V/r²h ................... (2)

where V is volume of cylinder, r is radius of cylinder and h is height of cylinder 

 

Since the volume of a cylinder varies jointly with the square or its radius and with its height, k in (1) and (2) is contant of proportion and it remains equal for all varying values of r and h

 

Also given that, cylinder A has a volume, V, of 254.34 cubic inches and has a radiu,s,r of 3 inches and a height,h, of 9 inches

 

Substituting these values of Cylinder A in (2)

k=254.34 / (3)²*9=254.34 /9*9=3.14

 

For cylinder B,  radius, r, of 4 inches and a height,h, of 5 inches and k=3.14

Substituting these values in (1)

Volume, V, of cylinder B=3.14*(4)²*5=251.2 cubic inches.