Question

1. art an art exhibit at a local museum features several similarly shaped metal cubes welded together to make a sculpture. the smallest cube has a edge length of 6 inches.

a. what are the edge lengths of the other cubes if the ratios of similarity to the smallest cube are 1.25, 4/3, 1.5, 7/4, and 2 respectively?
b. if the artist wanted to add a smaller cube with an edge length with a ratio of 2/3 to the sculpture, what size would the cube be?
c. why do you only have to find the length of one edge for each cube?

Explanation:

Step1: Calculate edge lengths for part a

Multiply the edge length of the smallest cube ($6$ inches) by each ratio.
For ratio $1.25$: $6\times1.25 = 7.5$ inches.
For ratio $\frac{4}{3}$: $6\times\frac{4}{3}=8$ inches.
For ratio $1.5$: $6\times1.5 = 9$ inches.
For ratio $\frac{7}{4}$: $6\times\frac{7}{4}=10.5$ inches.
For ratio $2$: $6\times2 = 12$ inches.

Step2: Calculate edge length for part b

Multiply the edge length of the smallest cube ($6$ inches) by the ratio $\frac{2}{3}$.
$6\times\frac{2}{3}=4$ inches.

Step3: Explain part c

Since all edges of a cube are equal in length. If we know the length of one edge, we know the lengths of all edges.

Answer:

a. $7.5$ inches, $8$ inches, $9$ inches, $10.5$ inches, $12$ inches.
b. $4$ inches.
c. Because all edges of a cube are of equal length.