AdaAda

Home / Library / Digital SAT Math: Algebra, Advanced Math & Geometry / Synthetic flashcard

What is the relationship between the linear scale factor $k$, the area ratio, and the volume ratio for similar geometric solids?

Study flashcard from the deck Digital SAT Math: Algebra, Advanced Math & Geometry.

Answer

If the ratio of corresponding linear dimensions is $k = \frac{L_1}{L_2}$, the ratio of surface areas is $k^2 = \frac{A_1}{A_2}$ and the ratio of volumes is $k^3 = \frac{V_1}{V_2}$.

Explanation

If a solid has its linear dimensions tripled ($k = 3$), its surface area increases by $3^2 = 9$ times, and its volume increases by $3^3 = 27$ times.

Synthetic content · Curated by Ada