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Grade 10 · Math · Geometry

10th grade Similar solids, and what changing a dimension does to perimeter, area, surface area and volume worksheet

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Similar solids, and what changing a dimension does to perimeter, area, surface area and volume

Grade 10 Math Worksheet - Challenge Me

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Circle the best answer, or write your answer on the line.

  1. The club can order one 12-inch pizza or three 6-inch pizzas. Milo compares the cheese. How many 6-inch pizzas have the same area as one 12-inch pizza?

  2. The club can order one 15-inch pizza or a stack of 5-inch pizzas. Noah compares the cheese. How many 5-inch pizzas have the same area as one 15-inch pizza?

  3. The club can order one 20-inch party pizza or a box of 4-inch mini pizzas. Pia compares the cheese. How many 4-inch pizzas have the same area as one 20-inch pizza?

  4. The club can order one 18-inch pizza or a tray of 6-inch pizzas. Ren compares the cheese. How many 6-inch pizzas have the same area as one 18-inch pizza?

  5. Zee's toy box holds 640 cubic inches. A similar mini toy box has every length one fourth as long. How much does the mini one hold, in cubic inches?

  6. Ari's glass pyramid holds 500 cubic cm. A similar mini glass pyramid has every length one fifth as long. How much does the mini one hold, in cubic cm?

  7. Bo's sand castle tower holds 448 cubic inches. A similar mini sand castle tower has every length half as long. How much does the mini one hold, in cubic inches?

  8. Esme has two similar cans that hold 8 and 64 cubic cm. The first one's surface area is 30 square cm. What is the second one's surface area, in square cm?

  9. Kira has two similar boxes that hold 16 and 128 cubic inches. The first one's surface area is 24 square inches. What is the second one's surface area, in square inches?

  10. Luz has two similar glass pyramids that hold 54 and 16 cubic cm. The first one's surface area is 45 square cm. What is the second one's surface area, in square cm?

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10th grade Similar solids, and what changing a dimension does to perimeter, area, surface area and volume worksheet – printable
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About this worksheet

Similar solids and changing dimensions. Every version has 10 questions, and the answer key prints on the second page.

What your child will learn

  • I can grow a length by k, an area by k × k and a volume by k × k × k.
  • I can find the scale factor from two volumes or two areas.
  • I can tell what a change in only the radius or only the height does to a volume.

Standard: G-GMD.A.3 (related), G-SRT.A.2

Words to know

similar solids: The same shape, with every length multiplied by one number.

scale factor (k): The number every length is multiplied by.

cube root: The number used three times to make it: the cube root of 64 is 4.

Common mistakes

Your child multiplied a length by the scale factor twice.

Your child added the scale factor instead of multiplying by it.

Your child grew an area or a volume by the scale factor only once. Draw a 1 by 1 square and double its sides: how many small squares fit now?

What to say

Ask: if a photo is made 3 times as wide, how many times as long is each edge?

Ask: is a copy 3 times as tall 3 more or 3 times as much?

Questions parents ask

What is the most common mistake with similar solids, and what changing a dimension does to perimeter, area, surface area and volume?

Your child multiplied a length by the scale factor twice.

How can I help my child with similar solids, and what changing a dimension does to perimeter, area, surface area and volume?

Ask: if a photo is made 3 times as wide, how many times as long is each edge?

Are these 10th grade math worksheets free to print?

Yes. All 6 printable versions at each level are free to print, with the answer key, and no account is needed.

More geometry

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