Direct proportion to the cube

Last updated on Apr 2, 2026

Scaffolded direct proportion to the cube worksheet

Direct proportion to the cube is when one quantity increases or decreases as the cube of another. This relationship often appears in physics, such as when calculating the volume of a sphere, which is directly proportional to the cube of its radius. Jump to the questions

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Question

y is directly proportional to p³

y = when p =

Find the equation for y and p

Step 1 - describe the relationship using the correct symbol

y ∝ p³

Step 2 - replace the symbol with the constant of proportionality, k

y = p³

Step 3 - substitute the values from the question into the equation

= k

Step 4 - rearrange the equation to isolate k

÷ = k

Step 5 - determine the value of k

k =

Step 6 - write the final equation linking y and p³

y = p³

Find y when p =

Step 1 - restate the equation

y = p³

Step 2 - substitute the value you know

y = ×

Step 3 - determine the final value of y

y =

Find p when y =

Step 1 - restate the equation

y = p³

Step 2 - substitute the value you know

= × p³

Step 3 - rearrange the equation to isolate p³

÷ = p³

Step 4 - calculate the value of p³

p³ =

Step 5 - calculate the value of p

p =