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

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Milo has two similar cans. The small one holds 5 cubic inches and the big one 320 cubic inches. What is the scale factor from small to big?
Noah has two similar sand pyramids. The small one holds 3 cubic feet and the big one 192 cubic feet. What is the scale factor from small to big?
Pia has two similar boxes. The small one holds 2 cubic inches and the big one 1458 cubic inches. What is the scale factor from small to big?
Ren has two similar gift boxes. The small one holds 4 cubic inches and the big one 108 cubic inches. What is the scale factor from small to big?
Tala has two similar boxes: surface areas 24 and 96 square inches. The small one holds 8 cubic inches. How much does the big one hold, in cubic inches?
Zee has two similar candles: surface areas 10 and 90 square inches. The small one holds 2 cubic inches. How much does the big one hold, in cubic inches?
Ari has two similar pyramids: surface areas 6 and 150 square feet. The small one holds 3 cubic feet. How much does the big one hold, in cubic feet?
Bo has two similar cans: surface areas 40 and 90 square cm. The small one holds 16 cubic cm. How much does the big one hold, in cubic cm?
Esme's old can has radius 2 cm and height 10 cm. The new one has radius 6 cm and height 10 cm. How many times as much does the new can hold?
Jun's old candle has radius 5 cm and height 3 cm. The new one has radius 10 cm and height 9 cm. How many times as much does the new candle hold?

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

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

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.

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?

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?

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.

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