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Scale Factor, Area and Volume - Printable Mathematics Worksheets year 10 - Wayground

Scale Factor, Area and Volume

10 questions

10th - 10th Grade

Mathematics

This Grade 10 mathematics worksheet develops understanding of how dilation scale factors affect the area and volume of two- and three-dimensional figures. Students solve four math-response problems involving circles, cones, and rectangular-prism boxes, including finding a scale factor from an area or volume and finding a new measurement after dilation. The worksheet also uses three multiple-choice questions, a matching activity, a fill-in-the-blank satellite scenario, and a dropdown item to reinforce that area changes by the square of the scale factor while volume changes by its cube. Real-world contexts involving beverage containers, solar panels, cereal boxes, and paint help students apply these relationships beyond formulas. It is designed for Grade 10 math instruction, independent practice, or assessment, and is available as a free printable worksheet with a complete answer key.

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Worksheets

Scale Factor, Area and Volume

Total questions: 10

Name
Class
Date
1.

Circle B is a dilation of Circle A by point D. The area of Circle B is 900π. The area of circle A is 36π. What is the scale factor?

2.

A beverage company manufactures and fills juice cans. They spend $0.09 on materials for each can and fill the can with $0.24 worth of juice.

The company wants to increase the size of the container and advertise it as the "Party Size". They approximate the cost of the materials for the new container to be $0.81. What will be the scale factor to use for the new contatiner?

a)

9

b)

13\frac{1}{3}

c)

3

d)

Not enough information.

3.

A cone has a surface area 360π in2in^2 and a volume of 800π in3in^3 . The cone is dilated and the surface area of the dilated cone is 2,250π in2in^2 . What is the dilated cone's volume in cubic inches?

4.

Match the following

3433\sqrt[3]{343}

7

2163\sqrt[3]{216}

6

5123\sqrt[3]{512}

8

273\sqrt[3]{27}

3

1253\sqrt[3]{125}

5

5.

A government agency is redesigning a satellite, or an object that goes in orbit around Earth. The surface of the satellite is covered with solar panels that supply the satellite with energy. The interior of the satellite is filled with scientific instruments. In the current design, the satellite has a surface area of 5.4 square feet and a volume of 1.2 cubic feet.

If the agency wants to increase the surface area to 48.6 square feet so the satellite can generate more energy, by what scale factor do they need to dilate the satellite? _



(a)  

6.

A food company is designing boxes for several products. Each box is a rectangular prism. The company makes a single serving cereal box that contains 1.2 ounces of cereal. They plan to make an extra large box for school cafeterias. The extra large box will be a dilation of the single serving box using a scale factor of 4. How many ounces of cereal will the extra large box contain in ounces of cereal?

7.

A food company is designing boxes for several products. Each box is a rectangular prism. The company also wants to offer a family size box of cereal. The family size box will be a dilation of the single serving 1.2-ounce box. It must contain 18.75 ounces of cereal. What scale factor does the company need to use for the family size box?

8.

When multiplying a length by a scale factor, does the scale factor change? ​ (a)   When adjusting the surface area of a solid, the scale factor must be ​ (b)   . When adjusting the volume of a solid, the scale factor must be​ (c)  

Choose from the below words
No
squared
cubed
Yes
Not relevant
left alone
9.

A solid with volume 12 cubic units is dilated by a scale factor of 53\frac{5}{3} . Find the volume of the image for each given value of 53\frac{5}{3} .

a)

20 units3units^3

b)

60 units3units^3

c)

253units3\frac{25}{3}units^3

d)

5009 units3\frac{500}{9}\ units^3

10.

It takes 2 ounces of paint to completely cover all 6 sides of a rectangular prism box which holds 15 cups of sugar. Double the dimensions of the box. Approximately how much paint would the new box need?

a)

8

b)

16

c)

4

d)

3

Answer Key

Scale Factor, Area and Volume

Total questions: 10

1.

55

2.
c)

3

3.

12500π12500\pi

4.

3433\sqrt[3]{343}

 - 

7

, 

2163\sqrt[3]{216}

 - 

6

, 

5123\sqrt[3]{512}

 - 

8

, 

273\sqrt[3]{27}

 - 

3

, 

1253\sqrt[3]{125}

 - 

5

5.
3
6.

76.876.8

7.

2.52.5

8.
No, squared, cubed
9.
d)

5009 units3\frac{500}{9}\ units^3

10.
a)

8

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FAQs

What does the Scale Factor, Area and Volume worksheet cover?

This Grade 10 worksheet focuses on applying dilation scale factors to area and volume. Its four math-response problems and mixed question types ask students to find scale factors from area or volume information, calculate dilated measurements, and distinguish between squared area changes and cubed volume changes in contexts such as cones, satellites, and cereal boxes.

How can I use this worksheet to teach scale factor changes in area and volume?

Begin by reviewing how a dilation changes one length, then have students predict whether an area or volume should use the scale factor, its square, or its cube. Use the circle, satellite, and cereal-box problems to model finding an unknown scale factor before assigning the matching, dropdown, and multiple-choice items for students to explain and apply the relationships independently.

What mistakes should I watch for when students complete this worksheet?

Students may use the area ratio or volume ratio as the linear scale factor instead of taking the appropriate square or cube root. They may also multiply volume by the scale factor or use a squared factor for volume, especially in the cereal-box and cone problems. In the paint and container scenarios, check that students identify whether the quantity represents surface area or volume before calculating.

How do I assign and grade this scale factor worksheet?

On Wayground, assign it either as a printable PDF or as a digital quiz; both versions include a complete answer key for the circle, cone, satellite, box, and mixed-format questions. Printable submissions can be graded by scanning student work with the Wayground for Teachers app.

How can I differentiate this scale factor, area, and volume worksheet?

In the worksheet’s Advanced Settings, adjust font spacing and font size to make the multi-step math-response problems and scenario text easier to read, enable a dyslexia-friendly font, or translate the worksheet into another language. These options apply across the worksheet’s math-response, multiple-choice, matching, fill-in-the-blank, and dropdown items.

Where can I find more worksheets like this on Wayground?

Wayground offers a broad collection of free printable worksheets and practice problems across subjects, with downloadable PDFs and answer keys to support essential skills and concepts. Browse more resources at https://wayground.com/en-us/worksheets.

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