Changes in scale

Find the volume of the cube

5m

V = Bh B = area of the base

B = 5 • 5B = 25

• 5125 m³25

B = 2500• 50

125,000 m³2500

V = Bh B = area of the baseB = 50 • 50

50m

after it has been dilated by a scale factor of 10

So, what’s the trick……. find the volume and then multiply it by the scale factor cubed

Find the volume of the coneafter it has been dilated by a scale factor of 4

5m

10m

13V = Bh

13V = •78.5•10

B = area of the baseB = π • 52

B = 78.5

V = 261.7

(scale factor )³=

4³64

so, how do you find the new volume?multiply the volume by the scale factor cubed

261.7 • 6416,748.8 m³

Find the surface area of the rectangular prism

5m

SA = Ph + 2B• 5

270 m2

(15+3+15+3)

50m

after it has been dilated by a scale factor of 10

So, what’s the trick…….find the surface area and then multiply it by the scale factor

squared

3m15m

+2 (153)

30m150m SA = Ph + 2B

27,000 m2

(150+30+150+30) +2 (15030)• 50

A rectangular prism has a volume of 78 cubic feet. If the dimensions of the prism are enlarged to five times the

original dimensions, what is the volume of the new prism?

V = 78 (5)3

V = 9,750 cubic feet

A triangular prism has a surface area of 432 square yards. If the dimensions of the prism are reduced to one third of the original dimensions, what is the

surface area of the new prism?SA = 432 (⅓)2

SA = 48 square yards

Which statement best describes the change in the perimeter of a rectangle if all of its side lengths

are multiplied by 4?A The new perimeter will be 12 times as large as the perimeter of the original rectangle

B The new perimeter will be 16 times as large as the perimeter of the original rectangle

C The new perimeter will be 4 times as large as the perimeter of the original rectangle

D The new perimeter will be 8 times as large as the perimeter of the original rectangle

Which statement best describes the change in the area of a

rectangle if all of its side lengths are multiplied by 4?

A The new area will be 12 times as large as the area of the original rectangle

B The new area will be 16 times as large as the area of the original rectangle

C The new area will be 4 times as large as the area of the original rectangle

D The new area will be 8 times as large as the area of the original rectangle

Which statement best describes the change in the volume of a

rectanglar prism if all of its side lengths are multiplied by 2?

A The new volume will be 12 times as large as the volume of the original prism

B The new volume will be 16 times as large as the volume of the original prism

C The new volume will be 4 times as large as the volume of the original prism

D The new volume will be 8 times as large as the volume of the original prism