Joint Variation

Question

The volume V of a cylinder varies jointly with the height h and the radius squared r^2, and V=157.00 cm^3 when h=2 cm and r^2= 25 cm^2. Find V when h=3 cm and r^2 = 36 cm^2

Answer 1

V ∝ h

V ∝ r²

 

Using these relationships, we can establish a formula.

 

 

V = Kr²h    where K is constant.

 

We need to find K using the initial values.

 

K = V / (r²h)

 

K = 157 cm³ / (25 cm²)(2 cm)

K = 157 cm³ / 50 cm³

K = 3.14

 

Notice that K is the value of pi.  Does the formula V = pi*r²h look familiar to you!

 

 

Next, find the value of V using the second set of values, now that K is known.

 

V = Kr²h

V = (3.14)(36 cm²)(3 cm)

V = 339.12 cm³

Answer 2

Hello Ghufran,

 

You should know the volume and surface area formulas for the common solids (sphere, cylinder, right cone, square pyramid, cube).

 

In this case, use V_cylinder = A_base * height = pi*r²*h. Just use that formula and round to 3 significant figures. What they want you to do, however, is multiply 157 by 1.5 (3/2) to account for the increased height and by 36/25 to account for the increased radius.

Try both methods to verify they match.  (They do.)

 

Eric Moline

McMinnville OR