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Ello, I just need three questions answered, that's all. Help much appreciated, thanks:)

1.A rectangle with an area of 4/7 m^2 is dilated by a factor of 7.What is the area of the dilated figure? Do not leave your answer as a fraction.

 

2.A prism with the base area of 8 cm^2 and a height of 6cm is dilated by a factor of 5/4. What is the volume of the dilated figure?

 

3.A prism with a volume of 875m^3 is scaled down to a volume of 448cm^3. What is the scale factor? Answer as a fraction or decimal in simplest form.

Guest Feb 20, 2017
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3+0 Answers

 #1
avatar+79881 
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1.A rectangle with an area of 4/7 m^2 is dilated by a factor of 7.What is the area of the dilated figure? Do not leave your answer as a fraction.

 

The area is increased by a square of the scate factor....so.....

 

(4/7) * 7^2  =

 

(4/7) * 49

 

(49/7) * 4  =

 

7 * 4  =

 

28 m^2

 

 

cool cool cool

CPhill  Feb 20, 2017
 #2
avatar+79881 
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2.A prism with the base area of 8 cm^2 and a height of 6cm is dilated by a factor of 5/4. What is the volume of the dilated figure?

 

The original volume will increase by a cube of the scale factor

 

Original volume  =  8 * 6  = 48cm^3

 

So

 

48 * (5/4)^3  =

 

[48 * 125] / 64  =

 

[48/64] * 125  =

 

(3/4) * 125  =

 

93.75 cm^3

 

 

cool cool cool

CPhill  Feb 20, 2017
 #3
avatar+79881 
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Call the scale factor, S  ....so...

 

448 * S^3  = 875

 

S^3  = 875/448

 

S^3  = 125 / 64       take the cube root of both sides

 

S  = 5/4

 

 

cool cool cool

CPhill  Feb 20, 2017

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