Similar Solids Effects on Change of Dimensions

A cone's surface area changed from 75 cm² to 300 cm² as it was enlarged proportionally. By what factor did the radius and height change?

• Increased by a factor of 1.5

• Increased by a factor of 3

• Increased by a factor of 4

• Increased by a factor of 2

A rectangular prism was scaled up, increasing its volume from 27 cm³ to 729 cm³. By what factor did each dimension change?

• Increased by a factor of 3

• Increased by a factor of 1.5

• Increased by a factor of 2

• Increased by a factor of 27

Tags

CCSS.7.G.B.6

A sphere was scaled down so its volume changed from 288π cm³ to 36π cm³. How did the radius change?

• Decreased by a factor of 1/4

• Decreased by a factor of 1/2

• Decreased by a factor of 1/8

• Decreased by a factor of 1/3

A cube’s surface area was reduced from 400 cm² to 100 cm² using a consistent scale. By what factor did the side length change?

• Decreased by a factor of 1/3

• Decreased by a factor of 1/5

• Decreased by a factor of 1/2

• Decreased by a factor of 1/4

Tags

CCSS.6.G.A.4

A cylinder was dilated so that its volume increased from 500 cm³ to 4000 cm³. What scale factor was applied to the radius and height?

• Increased by a factor of 8

• Increased by a factor of 3

• Increased by a factor of 2.5

• Increased by a factor of 2

A pyramid was scaled up, resulting in a change in surface area from 625 in² to 100 in². How did the height change?

• Decreased by a factor of 4/25

• Decreased by a factor of 1/3

• Decreased by a factor of 2/5

• Decreased by a factor of 1/5

Tags

CCSS.7.G.B.6

A triangular prism’s volume expanded from 108 m³ to 2916 m³ after a proportional scaling. By what factor did its dimensions change?

• Increased by a factor of 3

• Increased by a factor of 5

• Increased by a factor of 4

• Increased by a factor of 27

Tags

CCSS.7.G.B.6

A cube underwent a proportional reduction in size, and its surface area decreased from 729 cm² to 81 cm². What happened to the side length?

• Decreased by a factor of 1/2

• Decreased by a factor of 1/4

• Decreased by a factor of 1/3

• Decreased by a factor of 1/9

Tags

CCSS.6.G.A.4

The volume of a triangular prism increased from 90 cm³ to 270 cm³. The area of the triangular base stayed the same. How did the height of the prism change?

• The height was multiplied by 2

• The height was multiplied by 3

• The height was multiplied by 4

• The height was multiplied by 5

Tags

CCSS.7.G.B.6

A cylinder's volume decreased from 8000 cm³ to 1000 cm³. The radius remained constant. By what factor did the height change?

• The height was multiplied by 1/8.

• The height was multiplied by 1/6.

• The height was multiplied by 1/4.

• The height was multiplied by 1/2.

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3