Question

Often we need to use exponents to correctly model the variation in situations:

The volume of a cylinder varies jointly with the square of its radius and its height. Its
general equation looks like V = kr’h where k= some constant number for all cylinders
and V, rand h are variables representing volume, radius and height, respectively. When
the radius is 3 cm and height is 5 cm, the cylinder has a volume of 141.3 cm. Find the
volume when the radius is 6 cm and the height is 10 cm.

Answer 1

V = 1130.4 cm³

Explanation:

Given that V varies jointly with r² and h then the equation relating them is

V = kr²h ← k is the constant of variation

To find k use the condition when r = 3 and h = 5 then V = 141.3 , then

141.3 = k × 3² × 5 = 45k ( divide both sides by 45 )

k = 3.14 ← note approximation for π

V = 3.14r²h ← equation of variation

When r = 6 and h = 10, then

V = 3.14 × 6² × 10 = 3.14 × 36 × 10 = 1130.4 cm³