Changes in scale.

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Presentation transcript:

Changes in scale

Find the volume of the cube after it has been dilated by a scale factor of 10 50m 5m V = Bh B = area of the base V = Bh B = area of the base B = 50 • 50 B = 5 • 5 B = 2500 B = 25 25 • 5 2500 • 50 125,000 m³ 125 m³ find the volume and then multiply it by the scale factor cubed So, what’s the trick…….

Find the volume of the cone after it has been dilated by a scale factor of 4 (scale factor )³= 10m 4³ 5m 64 1 V = Bh B = area of the base 3 so, how do you find the new volume? B = π • 52 B = 78.5 multiply the volume by the scale factor cubed 1 V = •78.5•10 3 261.7 • 64 V = 261.7 16,748.8 m³

Find the surface area of the rectangular prism after it has been dilated by a scale factor of 10 50m 5m 3m 30m 15m 150m SA = Ph + 2B SA = Ph + 2B (15+3+15+3) • 5 +2 (153) (150+30+150+30) • 50 +2 (15030) 270 m2 27,000 m2 find the surface area and then multiply it by the scale factor squared So, what’s the trick…….

A rectangular prism has a volume of 78 cubic feet 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 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

Find the volume of the cube after it has been dilated by a scale factor of 10 5m V = Bh B = V = Bh B = B = B = B = B = • • m³ m³ find the ________ and then multiply it by the scale factor __________ So, what’s the trick……

Find the volume of the cone after it has been dilated by a scale factor of 4 (scale factor )³= 10m 5m 1 V = Bh B = 3 so, how do you find the new volume? B = • B = multiply the volume by the scale factor cubed V = • • • V = m³

Find the surface area of the rectangular prism after it has been dilated by a scale factor of 10 50m 5m 3m 30m 15m 150m SA = Ph + 2B SA = Ph + 2B ( ) • + (  ) ( ) • + (  ) m2 m2 find the __________________ and then multiply it by the scale factor ________________ So, what’s the trick…….

A rectangular prism has a volume of 78 cubic feet 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 =  ( )3 V = cubic feet

A triangular prism has a surface area of 432 square yards 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 =  ( )2 SA = square yards