# Lesson Worksheet: Similarity of Solids Mathematics • 8th Grade

In this worksheet, we will practice identifying similar solids and using similarity to find their dimensions, areas, and volumes.

**Q2: **

The figure shows two cubes. If the area of the smaller one is 143, and the sides are in the ratio , what is the surface area of the larger cube?

**Q7: **

A pair of regular triangular pyramids are similar. Pyramid A has a base side of 17 inches and a slant height of 20 inches, whereas pyramid B has a base side of inches and a slant height of 42 inches. Determine the value of .

**Q8: **

A pair of rectangular prisms are similar. Prism is 104 by 32 by 24 inches, while prism is 26 by 8 by inches. Find.

**Q9: **

A pair of cylinders are similar. Cylinder A has a base radius of 29 inches and a length of 6 inches, and cylinder B has a base radius of inches and a length of 18 inches. Determine the value of .

**Q10: **

The surface areas of two similar solids are 64 square yards and 361 square yards. Find the ratio of their linear measures.

- A
- B
- C
- D
- E

**Q11: **

The given pair of rectangular prisms are similar. If the surface area of the smaller rectangular prism is 310 yd^{2}, determine the surface area of the larger one.

**Q12: **

A cone has a volume of 11,756 cubic centimeters. Suppose that its dimensions were reduced as the figure shows, find the volume of the resulting cone.

**Q13: **

What is the scale factor of two similar cylinders whose volumes are 1,331 and 1,728 cubic meters?

- A
- B
- C
- D
- E

**Q16: **

Two similar cones have radii of 5 millimeters and 10 millimeters. What is the ratio of the surface area of the small cone to the surface area of the large one?

- A
- B
- C
- D4
- E2

**Q17: **

Two similar cones have surface areas of 768 and 363. What is the ratio of the height of the larger cone to that of the smaller one?

- A
- B
- C
- D
- E