Similar Shapes and Scale

What is the volume ratio of two pyramids with surface areas of 80 cm² and 245 cm²?

• 4/7

• 16/49

• 64/343

• 256/2401

By what factor would the volume of a triangular prism decrease if the dimensions (side lengths) were decreased by a factor of 1/3?

• 1/3

• 1/6

• 1/9

• 1/27

Mrs. Smith made a cake that has a diameter of 7 inches and a height of 5.5 inches, as shown. She wants to design a new cake by dilating the dimensions of the original cake by a scale factor of 1.4.

What will be the diameter of the new cake?

• 7.7 in

• 9.8 in

• 6.2 in

• 12.5 in

Triangle ABC is similar to triangle XYZ. What is the value of p in centimeters?

• 8 cm

• 20 cm

• 0.8 cm

• .2 cm

Pentagon ABCDE was used to create pentagon RSTUV. Based on the given information, what scale factor was used to create pentagon RSTUV?

• 2.5 cm

• 3 cm

• 39.6 cm

• 27.5 cm

• 7.74 cm

• 9.18 cm

• 10.7 cm

• 11.7 cm
  

The bases of the two similar trangular prisms shown below are equilateral triangles. What is the value of x in centimeters?

• 11.2 cm

• 78.4 cm

• 28 cm

• 19.6 cm

A tree casts a shadow 10 feet long. A 5 foot woman casts a shadow 4 feet long. The triangle shown for the woman and her shadow is similar to the triangle shown for the tree and its shadow. How tall is the tree?

• 12.5 ft

• 11 ft

• 8 ft

• 16 ft

Triangle PQR is similar to triangle XYZ. What is the length of XZ?

• 13.5 in

• 12 in

• 4 in

• 20 in

A rectangle has a length of 8.5 inches and a width of 4 inches. This rectangle is dilated by a scale factor of 2.5 to create a new rectangle. What is the length of x for the new rectangle.

• 8.5 in

• 10 in

• 12.5 in

• 4 in