Effects of Changing the Dimensions of a Figure Assignment and Quiz

Sinclair applied a dimensional change to a trapezoid with a height of 5 and base lengths 3 and 7 to determine the effect a proportional change has on the area. His work is shown below. Use Sinclair's work to answer the questions and complete the statements. How did Sinclair come up with the dimensions 1, 7/3, and 5/3 in step 2? He multiplied the original dimensions by a scale factor of ________. What can Sinclair conclude about the effect on the trapezoid's area from his comparison? The changes created an area times the original area.

1/3 1/9

A rectangle is dilated by a factor of 1/5. The area of the new rectangle is 4 square yards. What could be the dimensions of the original rectangle?

10 yards by 10 yards

The circle will be dilated by a scale factor of 6. es026-1.jpg What is the value for n if the expression nes026-2.jpg represents the circumference of the circles in inches?

108

Consider this triangle and the formula for the area of a triangle. What is the area of the triangle after applying a dilation by a scale factor of 2? Describe the effects.

126 cm2. The area of the new triangle is 4 times the area of the original triangle.

A rectangular prism has sides of 4 cm, 2.5 cm, and 5.5 cm. The figure is dilated by a scale factor of 3. What is the volume of the new prism? What can be concluded about the effect of the change on the new volume? The new volume is _________ times the original volume.

1485 27

A rectangle has a width of 5 inches and a length of 9 inches. What will be the new dimensions of the rectangle after it is dilated by a scale factor of 3?

15 inches by 27 inches

A rectangle has an area of 6 square meters. What will be the area of the rectangle if each side length is increased by a factor 5?

150 square meters

Consider this square pyramid. Recall the volume can be found using the formula V = 1/3Bh What is the volume of the pyramid after dilating by a scale factor of 1/4? Describe the effects.

16 m3. The volume of the new pyramid is the volume of the original pyramid times 1/64

The perimeter of the rectangle is __________ cm. If the rectangle is dilated by a scale factor of 6 to create a new rectangle, the new dimensions are __________. The perimeter of the new rectangle is __________ cm. When comparing the new perimeter to the original perimeter, the new perimeter is __________.

28 54 cm and 30 cm 168 6 times greater

The volume of a prism changes from 20 to 540 after a dilation. What was the scale factor of the dilation?

3

The triangle will be enlarged by a scale factor of 10. mc018-1.jpg What will be the area of the new triangle?

3,500 square cm

The cube will be enlarged by a scale factor of 8. mc019-1.jpg What will be the volume of the new cube?

4,096 cubic units

A cardboard box has a volume that is 6,336 cubic inches. A company creates a new design with the same proportions, but instead the dimensions are 1/4 the dimensions. Explain how you can find the volume of the new design without knowing the dimensions.

Cube the scale factor 0.25. Then multiply the volume of the box by 0.015625.

A circle with a radius of 1/2 ft is dilated by a scale factor of 8. Which statements about the new circle are true? Check all that apply.

The length of the new radius will be 4 feet. The new circumference will be 8 times the original circumference. The new area will be 64 times the original area. The new circumference will be 8/╓ feet. The new area will be 16╓ square feet.

A rectangle has a length of 12 mm and a width of 15 mm. A new rectangle was created by multiplying all of the dimensions by a scale factor of 1/3 Which statement best describes the change in the perimeter of the new rectangle?

The new perimeter will be 1/3 times the perimeter of the original rectangle.

Consider this circle and recall the formulas for circumference and area: The circle is dilated by a scale factor of 3/4. What can be concluded of the effect on the circle? Check all that apply.

The new radius is 6 inches. The new circumference is 12╓ inches. The new area is the original area times the square of 3/4.

A new square has dimensions that are 1/10 the size of the original square. What statements are true? Select all that apply.

The perimeter of the new square is 1/10 times the perimeter of the original square. The area of the new square is 1/100 times the area of the original square.

Compare and contrast the effects that a proportional dimension change has on perimeter and area of figures.

The perimeter will change by the same scale factor. The area will change by the square of the scale factor

How will the volume of the pyramid change if each side is multiplied by a factor of 1/2? mc008-2.jpg

The volume will be 1/8 times the volume.

How will the volume of the prism change if each side is increased by a factor of 4? mc007-1.jpg

The volume will be 64 times the original volume.