EOM 3

Use whole squares and half squares of the shaded polygonal regions to find the average estimate for the area inside the curve.

The average estimate for the area inside the curve is ____ square units.

• 9.5

• 22.5

• 16

• 32

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G.GMD.1

Wes has a small fish tank in the shape of a right rectangular prism.  It has a base 12 in. × 6 in. and height 8 in. It is filled with water to a height of 5 in. He wants to put 4 identical fake tree stumps in the fish tank.  A sketch of a tree stump is shown.

About how many inches will the water level rise if Wes puts 4 tree stumps in the tank?  Round your answer to the nearest tenth of an inch.

• 1.8

• 2.4

• 0.9

• 5.3

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The density of pure iron is 7.874 g/cm³.  A piece of steel made of pure iron and other types of iron is in the shape of a rectangular pyramid.  The rectangular pyramid has a base edge length of 4 cm, a base edge width of 9 cm, a height of 5 cm, and a mass of 425 g.  What is the difference between the density of pure iron and the density of the steel rectangular pyramid?  Round your answer to the nearest thousandth.

• 7.874

• 0.764

• 7.083

• 425/60

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G.MG.2

A rectangular prism has a base with edge length 40 units, edge width 3 units, and height of 30 units.  A triangular prism has a right triangular base with legs that are 60 units and 4 units long and a height of 30 units.

What is the volume of the triangular prism?

• 120 units³

• 1,200 units³

• 3,600 units³

• 7,200 units³

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G.GMD.1

Use Cavalieri’s principle to explain why the rectangular prism has the same volume as the triangular prism.

Evaluate responses using AI:

OFF

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A candy company is designing a container for its new candy creation.  Consider the cost per cubic centimeter of these three proposed designs.

1.  A pyramid-shaped container with a square base that is 10 cm on each side and with height 20 cm.  This container would cost $5.30.

2.  A cone-shaped container with a radius of 5 cm and height 20 cm.  This container would cost $3.90.

3.  A cylinder-shaped container with a radius of 5 cm and height 15 cm.  This container would cost $7.00.

The least expensive container in terms of cost per cubic centimeter is

• pyramid

• cone

• cylinder

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G.MG.3

A candy company is designing a container for its new candy creation.  Consider the cost per cubic centimeter of these three proposed designs.

1.  A pyramid-shaped container with a square base that is 10 cm on each side and with height 20 cm.  This container would cost $5.30.

2.  A cone-shaped container with a radius of 5 cm and height 20 cm.  This container would cost $3.90.

3.  A cylinder-shaped container with a radius of 5 cm and height 15 cm.  This container would cost $7.00.

For PYRAMID, what is the cost per cubic centimeter?  Round your answer to the nearest thousandth.

• 0.008

• 0.007

• 0.006

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G.MG.3

An ice cream cone measures 2 in. across the opening of the cone.  Two hemisphere-shaped scoops of ice cream, which have diameters of 2 in., are placed on top of the cone.  As the ice cream melts, it begins to fill the ice cream cone.  How deep must the ice cream cone be so that the melted ice cream will fill the cone exactly to the top without overflowing?

• 2 in

• 1 in

• 4 in

• 8 in

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