Inverse proportion to the cube

Last updated on Apr 3, 2026

Inverse proportion to the cube worksheet

Inverse proportion to the cube occurs when one quantity decreases in proportion to the cube of another quantity. This relationship is commonly seen in physics, such as in gravitational or electrostatic forces, where the strength of the force diminishes rapidly with increasing distance. Understanding this concept is essential for solving problems where changes become dramatically smaller as one value grows larger. Jump to the questions

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Question

y is inversely proportional to p³

y is when p is

Find the equation for y and p

Step 1 - describe the relationship using the correct symbol

y ∝ 1 / 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

= ÷

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 - determine the value of p³

p³ =

Step 5 - calculate p

p =