Exam 19: Ratio, Proportion, and Variation

The lateral surface area of a cylinder varies jointly as the radius and the height. If the height is increased by $20 \%$ and the radius is increased by $40 \%$ , by what percent does the lateral surface area increase?

If $y$ varies jointly as $w$ and $x$ , by what factor will $y$ change if $x$ is quadrupled and $w$ is halved?

If $y$ is directly proportional to the cube root of $x$ and inversely proportional to the square root of $w$ , and $y$ is 10 when $x=250$ and $w=540$ , find $y$ when $x=3500$ and $w=5500$ .

Determine the values for $x$ and $y$ given that $x: 5: 7=10: y: 35$ .

If $y$ is directly proportional to the $5 / 2$ power of $x$ and inversely proportional to $w$ squared, and $y$ is 322 when $x$ is 957 and $w$ is 108, find the constant of proportionality and write the complete equation for $y$ in terms of $x$ and $w$ .

If $y$ is directly proportional to the square root of $x$ and inversely proportionally to the cube root of $w$ , and $y$ is 10 when $x=80$ and $w=30$ , find $y$ when $x=5$ and $w=3$ .

The frequency of a sound wave travelling through a medium varies inversely as the wavelength. If the frequency is $433 \mathrm{~Hz}$ when the wavelength is $0.700 \mathrm{~m}$ , what is the frequency when the wavelength is $1.20 \mathrm{~m}$ ?

Two prisms are similar. The volume of one is $157.5 \mathrm{~m}^{3}$ while the other has a volume of $53.2 \mathrm{~cm}^{3}$ . If the surface area of the smaller prism is $89.4 \mathrm{~cm}^{2}$ , what is the surface area of the larger prism?

Two polygons are similar. One has area $56.5 \mathrm{~cm}^{2}$ and the other one has area $175 \mathrm{~cm}^{2}$ . A side length in the smaller polygon is $4.30 \mathrm{~cm}$ . What is the length of the corresponding side in the larger polygon?

Divide $\$ 240$ into two parts where the smaller is to the greater as 3 is to 5 .

A certain light source produces an illumination of 235 lumens on a surface. Find the illumination of the surface when the source is moved 3.20 times closer.

If a certain machine can make 172 parts in 38 minutes, how many parts can it make in 8 hours?

Find the missing quantity: $\frac{12 x}{?}: \frac{1.8 x}{0.3}$

Find the mean proportional between 4 and 100 .

The actual distance between the two cities is $128 \mathrm{~km}$ , but they are $2.50 \mathrm{~cm}$ apart on the map. Find the actual distance between two points that are $12.0 \mathrm{~cm}$ apart on the same map.

Assume $y$ is directly proportional to $x$ and $y$ is 75.4 when $x$ is 1.45 . (a) Find the constant of proportionality. (b) Write the equation $y=\mathrm{f}(x)$ . (c) Find $y$ when $x=16.3$ . (d) Find $x$ when $y=234$ .

Assume $y$ is directly proportional to the 4 th power of $x$ and has a value of 155.58 when $x$ is 4.2 . (a) Find the constant of proportionality. (b) Write the equation $y=\mathrm{f}(x)$ . (c) Find $y$ when $x=0.4$ . (d) Find $x$ when $y=75.03$ .

If $y$ is inversely proportional to the cube of $x$ and $y$ is 0.50 when $x$ is 2.0 , find $y$ when $x$ is 5.0 .

Find the mean proportional between 2 and 72 .

If a body falls $225 \mathrm{~m}$ in the first five seconds after it is dropped, how far does it fall in the next five seconds?