Surface Area and Volume of Three Dimensional Figures

a three-dimensional figure with two parallel bases that are the same size and shape. The other faces are parallelograms. Its named by the shape of its bases.

• pyramid

• prism

a three-dimensional figure whose base is a polygon and whose other faces are triangles.

• pyramid

• prism

The three-dimensional figure is composed of three congruent rectangular prisms with the measurements shown. What is the surface area, in square centimeters, of the figure?

Mathematical Equivalence

ON

What is the volume of the prism in cubic inches?

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Find the volume of the figure.

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What is the surface area of the rectangular prism shown?

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The object shown is made of twenty-four rectangular prisms with dimensions of 8 cm by 11 cm by 14 cm. What is the volume, in cubic centimeters, of the object?

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What is the volume, in cubic yards, of a cylinder with a diameter of 26 yards and a height of 19 yards? Round your answer to the nearest hundredth.

Mathematical Equivalence

ON

June has two similar rectangular boxes. If the sides of one box are 3 times the lengths of the corresponding sides of the other box, which of the following is true?

• The volume of one box is 3 times the volume of the other.

• The volume of one box is 6 times the volume of the other.

• The volume of one box is 9 times the volume of the other.

• The volume of one box is 27 times the volume of the other.

A horizontal slice of the rectangular prism is made. The slice is parallel to rectangle BCGF. Which of these statements are true? Choose all that are correct.

• The slice must have two sides of length 2.

• The perimeter of the slice is 20 units.

• The slice could have two sides of length 6.

• The slice is a rectangle.

• The area of the slice is 4 square units.