User:
• Matrices
• Algebra
• Geometry
• Funciones
• Trigonometry
• Coordinate geometry
• Combinatorics
 Suma y resta Producto por escalar Producto Inversa
 Monomials Polynomials Special products Equations Quadratic equations Radical expressions Systems of equations Sequences and series Inner product Exponential equations Matrices Determinants Inverse of a matrix Logarithmic equations Systems of 3 variables equations
 2-D Shapes Areas Pythagorean Theorem Distances
 Graphs Definition of slope Positive or negative slope Determine slope of a line Ecuación de una recta Equation of a line (from graph) Quadratic function Posición relativa de dos rectas Asymptotes Limits Distancias Continuity and discontinuities
 Sine Cosine Tangent Cosecant Secant Cotangent Trigonometric identities Law of cosines Law of sines
 Ecuación de una recta Posición relativa de dos rectas Distancias Angles in space Inner product

Volume Similar Solids

# Volume Similar Solids

The figures below are similar.

What is the volume of the smaller cone?

The following proportion applies to similar solids:

$(\frac{a}{b})^3=\frac{V_1}{V_2}$ where $\frac{a}{b}$ is the ratio of the corresponding dimensions, and $\frac{V_1}{V_2}$ is the ratio of the volumes.

Find the cube of the ratio of the corresponding dimensions:

$(\frac{a}{b})^3=(\frac{2}{5})^3=\frac{8}{125}$

Find the ratio of the volumes:

$\frac{V_1}{V_2}=\frac{V_1}{8,000}$

Use these two ratios to set up a proportion and solve for V1.

 $\frac{8}{125}$
=
 $\frac{V_1}{8,000}$

 8 × 8,000
=
125
 V1
Find the cross products

64,000 =
125
 V1
Simplify

 64,000 ÷ 125
=
125
 V1
÷ 125
Divide both sides by 125

512 =
 V1

The volume of the smaller cone is 512 cubic metres.

The figures below are similar.
What is the volume of the smaller cilynder?

 20 yd 4 yd 50240 yd3

V1 = yd3