4. Geometry
Similarity Scaling — Quiz
Test your understanding of similarity scaling with 5 practice questions.
Practice Questions
Question 1
A solid metal sphere with a radius of $R$ is melted down and recast into a smaller similar sphere with a radius of $\frac{R}{3}$. What is the ratio of the surface area of the original sphere to the surface area of the new sphere?
Question 2
A rectangular swimming pool has a length of $20$ meters, a width of $10$ meters, and a depth of $2$ meters. If a similar, smaller pool is built with a length of $15$ meters, what is the volume of the smaller pool?
Question 3
Two similar cylindrical pipes have a ratio of their capacities (volumes) of $1:8. If the diameter of the larger pipe is $12$ cm, what is the diameter of the smaller pipe?
Question 4
A sculptor creates a miniature model of a statue at a scale of $1:25. If the actual statue has a surface area of $$100 \text{ m}^2$$, what is the surface area of the miniature model in square centimeters?
Question 5
Two similar pyramids have a ratio of their base areas of $4:9. If the height of the smaller pyramid is $10$ cm, what is the height of the larger pyramid?