IXL - Surface area and volume: changes in scale (Geometry practice)

Look at this cube:

6 yd

If the side lengths are tripled, then which of the following statements about its volume will be true?

The new volume will be

times the old volume.

The new volume will be

times the old volume.

The new volume will be

times the old volume.

The new volume will be

times the old volume.

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Learn with an example

question

Look at this rectangular prism:

3 yd

2 yd

1 yd

If all three dimensions are doubled, then which of the following statements about its surface area will be true?

The ratio of the new surface area to the old surface area will be

4:1

The ratio of the new surface area to the old surface area will be

16:1

The ratio of the new surface area to the old surface area will be

9:1

The ratio of the new surface area to the old surface area will be

2:1

solution

You can solve this problem without using the measurements given in the diagram.

The original rectangular prism had this surface area:

S = 2(lw + lh + wh)

The new rectangular prism will have 2 times the length, 2 times the width, and 2 times the height. Since the original dimensions were l, w, and h, the new dimensions will be 2l, 2w, and 2h. Calculate the surface area:

S	=	2[(2l)(2w) + (2l)(2h) + (2w)(2h)]

	=	2(4lw + 4lh + 4wh)

	=	2 · 4(lw + lh + wh)

	=	8(lw + lh + wh)

Divide the new surface area by the original surface area and simplify.

new surface area

original surface area

8(lw + lh + wh)

2(lw + lh + wh)

Write the result as a ratio.

4 → 4:1

The ratio of the new surface area to the old surface area will be

4:1

Looking for more? Try these:

Lesson: Surface area formulas

Lesson: Volume formulas

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Teacher tools

Work it out

Not feeling ready yet? These can help:

D.2Volume

D.3Surface area

L.1Understanding ratios

Lesson: Surface area formulas

Lesson: Volume formulas

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