#1
Which of the following statements best defines similarity between geometric solids?
Having the same shape but different sizes
ExplanationSimilarity refers to geometric figures having identical shapes but varying sizes.
#2
If two rectangular prisms are similar, what can we say about their corresponding sides?
They have proportional lengths
ExplanationSimilarity ensures that corresponding sides of geometric figures are in proportion to each other.
#3
If the ratio of volumes of two similar cylinders is 8:27, what is the ratio of their corresponding radii?
2:3
ExplanationThe ratio of volumes between similar solids is equal to the cube of the ratio of their corresponding linear measures.
#4
Two cones are similar. If the ratio of their radii is 2:3, what is the ratio of their volumes?
8:27
ExplanationVolume ratio between similar solids equals the cube of the ratio of their corresponding linear measures.
#5
If the scale factor between two similar cubes is 3:4, what is the ratio of their surface areas?
9:16
ExplanationThe ratio of surface areas between similar figures equals the square of the scale factor applied.
#6
If the scale factor between two similar cones is 2:5, what is the ratio of their heights?
5:2
ExplanationThe ratio of heights between similar figures equals the reciprocal of the ratio of their corresponding linear measures.
#7
If a cube has a surface area of 54 square units, what is the length of one edge?
6 units
ExplanationSurface area of a cube equals 6 times the square of its edge length.
#8
If two cylinders are similar and the ratio of their radii is 1:3, what is the ratio of their volumes?
1:9
ExplanationVolume ratio between similar solids equals the cube of the ratio of their corresponding linear measures.
#9
If the lateral surface area of a cylinder is 36π square units and its height is 6 units, what is the radius of the cylinder?
3 units
ExplanationLateral surface area of a cylinder equals the product of its height and circumference.
#10
If the volume of a cube is 64 cubic units, what is the volume of a cube that is similar to it with a scale factor of 2?
256 cubic units
ExplanationThe volume of a similar figure scales with the cube of the scale factor applied.
#11
A cylinder has a volume of 125π cubic units. If the cylinder is similar to another cylinder with a scale factor of 2, what is the volume of the second cylinder?
1000π cubic units
ExplanationVolume of similar figures scales with the cube of the scale factor applied.
#12
If the ratio of the volumes of two similar spheres is 8:27, what is the ratio of their radii?
2:3
ExplanationVolume ratio between similar solids equals the cube of the ratio of their corresponding linear measures.
#13
If two pyramids are similar and the ratio of their volumes is 1:8, what is the ratio of their heights?
2:1
ExplanationVolume ratio between similar solids equals the cube of the ratio of their corresponding linear measures.
#14
Two rectangular prisms are similar. If the ratio of their volumes is 8:27, and the dimensions of the smaller prism are 2x3x4, what are the dimensions of the larger prism?
12x18x24
ExplanationVolume ratio between similar solids equals the cube of the ratio of their corresponding linear measures.
#15
If the surface area of a sphere is 144π square units, what is the radius of the sphere?
12 units
ExplanationSurface area of a sphere equals 4 times π times the square of its radius.
#16
A cube has a volume of 64 cubic units. If the cube is similar to another cube with a scale factor of 3, what is the volume of the second cube?
1,728 cubic units
ExplanationVolume of similar figures scales with the cube of the scale factor applied.