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MA.912.G.7.7 Effects of Dimension Change on Measurement

 

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Two-Dimensional

Three-Dimensional

Trig & Discrete Math

In Your Text

Section 12-2; 830-837
Section 12-3; 838-846
Section 12-4; 847-854
Extend 12-4; 855
Section 12-5; 857-863
Section 12-6; 864-871

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What You Need To Know...

Dimension changes affecting the surface area and volume of geometric solids.

  1. The benchmark will be assessed using MC (Multiple Choice) and FR (Fill in Response) items.
  2. Items may request the affect (perimeter, area, surface area, volume) of changed parameters (dimensions) in right prisms, right circular cylinders, spheres, right pyramids, right circular cones, and/or composites of these solids.

Example One

Kendra has a compost box that has the shape of a cube.  She wants to increase the size of the box by extending every edge of the box by half of its original length.  After the box is increased in size, which of the following statements is true?

  1. The volume of the new compost box is exactly 112.5% of the volume of the original box.
  2. The volume of the new compost box is exactly 150% of the volume of the original box.
  3. The volume of the new compost box is exactly 337.5% of the volume of the original box.
  4. The volume of the new compost box is exactly 450% of the volume of the original box.

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Example Two

A city is planning to replace one of its water storage tanks with a larger one.  The city's old tank is a right circular cylinder with a radius of 12 feet and a volume of 10,000 cubic feet.  The new tank is a right circular cylinder with a radius of 15 feet and the same height as the old tank.  What is the maximum number of cubic feet of water the new storage tank will hold?

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CLICK HERE FOR SOLUTION

Additional Examples

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Area and Perimeter
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Surface & Lateral Area
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Volume
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Reference Sheet

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