Quiz about Geometry | Unit 5 | Lesson 7: The Root of the Problem | Practice Problems

Question 1

A solid with volume 8 cubic units is dilated by a scale factor of $$k$$ to obtain a solid with volume $$V$$ cubic units. Find the value of $$k$$ which results in an image with each given volume.

Accepted Answer

216 cubic units

Accepted Answer

1,000 cubic units

Answer

1 cubic unit

Question 2

A solid has volume 7 cubic units. The equation $$k=\sqrt[3]{\frac{V}{7}}$$ represents the scale factor of $$k$$ by which the solid must be dilated to obtain an image with volume $$V$$ cubic units. Select all points which are on the graph representing this equation.

Accepted Answer

A: $$(0,0)$$

Accepted Answer

D: $$(7,1)$$

Accepted Answer

G: $$(56,2)$$

Answer

B: $$(1,1)$$

Answer

C: $$(1,7)$$

Question 3

A solid with surface area 8 square units is dilated by a scale factor of $$k$$ to obtain a solid with surface area $$A$$ square units. Find the value of $$k$$ which leads to an image with each given surface area.

Accepted Answer

512 square units

Accepted Answer

8 square units

Answer

$$\frac{1}{2}$$ square unit

Question 4

A solid with volume 8 cubic units is dilated by a scale factor of $$k$$ . Find the volume of the image for each given value of $$k$$ .

Accepted Answer

$$k=\frac{1}{2}$$

Accepted Answer

$$k=1$$

Accepted Answer

$$k=1.5$$

Answer

$$k=0.6$$

Question 5

A figure has an area of 9 square units. The equation $$y=\sqrt{\frac{x}{9}}$$ represents the scale factor of $$y$$ by which the solid must be dilated to obtain an image with area of $$x$$ square units. Select all points which are on the graph representing this equation.

Accepted Answer

A: $$(0,0)$$

Accepted Answer

E: $$(9,1)$$

Accepted Answer

H: $$(36,2)$$

Answer

B: $$(1,1)$$

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