Question

9.
The Volume (V) of a cone varies jointly as its height (h) and the square of its radius (r). Find
the percentage change in V if r is decreased by 10% and h is increased by 20%.

Answer 1

The percentage change in V if r is decreased by 10% and h is increased by 20% is 64.8%

If the Volume (V) of a cone varies jointly as its height (h) and the square of its radius (r), this is expressed as:

$V \alpha hr^2\\V = khr^2$

h is the height

r is the radius

k is the constant of proportionality

If r is decreased by 10% and h is increased by 20%, the new height will be 0.8h and the new radius is 0.9r

The new volume will be:

$V_2 = k(0.9r)^2(0.8h)\\V_2 = 0.648krh$

Divide both expressions to get the percentage change in volume:

$\frac{V_2}{V} =\frac{0.648kr^2h}{kr^2h}\\\frac{V_2}{V} = 0.648\\\frac{V_2}{V} =64.8%$

Hence the percentage change in V if r is decreased by 10% and h is increased by 20% is 64.8%

Learn more here: https://brainly.com/question/11613758