List of top Quantitative Aptitude Questions on Similar Triangles and Mensuration asked in SNAP

In triangle \(ABC\), point \(M\) lies on side \(AC\) and point \(N\) lies on side \(BC\), such that \(MN\) is parallel to \(AB\) (so triangle \(CMN\) is the smaller triangle near vertex \(C\), and \(ABNM\) is the trapezium formed below it). If the area of trapezium \(ABNM\) is twice the area of triangle \(CMN\), what is the ratio \(CM : AM\)?
The radius of a wire is decreased to one-third, and its volume remains the same. The new length is how many times the original length?
A solid sphere is melted and recast into a right circular cone with a base radius equal to the radius of the sphere. What is the ratio of the height to the radius of the cone so formed?
One side of an equilateral triangle is 24 cm. The midpoints of its sides are joined to form another triangle, whose midpoints are in turn joined to form still another triangle. This process continues indefinitely. Find the sum of the perimeters of all the triangles.
Three parallel lines are cut by two transversals as shown in the given figure. If AB = 2 cm, BC = 4 cm and DE = 1.5 cm, then the length of EF is:
A rectangular park 60 m long and 40 m wide has two concrete crossroads running in the middle of the park, and the rest of the park is used as a lawn. If the area of the lawn is 2109 sq. m, what is the width of the road?
A 4 cm cube is cut into 1 cm cubes. What is the percentage increase in the surface area after such cutting?
Two people were walking in opposite directions from the same starting point. Both of them walked 6 miles forward, then took a right turn and walked 8 miles. How far is each of them from their starting position?
Inside a triangular park, a flower bed forms a triangle similar to the park's boundary. A uniform path runs around the flower bed, so that each side of the park is exactly double the corresponding side of the flower bed. What is the ratio of the area of the path to the area of the flower bed?