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.

Q1:

Given that these two triangular prisms are similar, find the value of π‘₯.

Q2:

The figure shows two cubes. If the area of the smaller one is 143, and the sides are in the ratio 1∢5, what is the surface area of the larger cube?

Q3:

If the pair of triangular prisms are similar, and the surface area of the smaller one is 198 yd2, find the surface area of the larger one.

Q4:

A pair of cones are similar. Cone A has a base radius of 17 cm and a slant height of 20 cm, whereas cone B has a base radius of π‘₯ cm and a slant height of 48 cm. Determine the value of π‘₯.

Q5:

A pair of square pyramids are similar. Pyramid A has a base side of 125 in and a slant height of 160 in, and pyramid B has a base side of π‘₯ in and a slant height of 32 in. Determine the value of π‘₯.

Q6:

If the two given pyramids are similar and the volume of the larger pyramid is 160 m3, find the volume of the smaller one.

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 π‘₯ inches and a slant height of 42 inches. Determine the value of π‘₯.

Q8:

A pair of rectangular prisms are similar. Prism 𝐴 is 104 by 32 by 24 inches, while prism 𝐡 is 26 by 8 by π‘₯ inches. Findπ‘₯.

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 π‘₯ inches and a length of 18 inches. Determine the value of π‘₯.

Q10:

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

  • A1927
  • B827
  • C64425
  • D819
  • E64361

Q11:

The given pair of rectangular prisms are similar. If the surface area of the smaller rectangular prism is 310 yd2, 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?

  • A1123
  • B1223
  • C1,3313,059
  • D1112
  • E1,3311,728

Q14:

Given that the volume of the smaller cube is 8 cubic feet, determine the volume of the larger cube.

Q15:

Cones 𝐴 and 𝐡 are similar. Calculate the volume of cone 𝐡.

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?

  • A14
  • B14
  • C12
  • 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?

  • A121256
  • B256121
  • C1611
  • D1116
  • E16121

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