Lesson 12

Volume of Right Prisms

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Problem 1

  1. Select all the prisms.
  2. For each prism, shade one of its bases.
    Five figures. Figure A, prism with triangle base. Figure B, prism with pentagon base. Figure C, prism with triangle base. Figure D, prism with triangle base. Figure E, pyramid with a rectangle base.

Solution

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Problem 2

The volume of both of these trapezoidal prisms is 24 cubic units. Their heights are 6 and 8 units, as labeled. What is the area of a trapezoidal base of each prism?

Two prisms.  The first has a trapezoid for a base and a height of 6.  The second has a trapezoid base and a height of 8.

 

Solution

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Problem 3

Two angles are complementary. One has a measure of 19 degrees. What is the measure of the other?

Solution

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(From Unit 7, Lesson 2.)

Problem 4

Two angles are supplementary. One has a measure that is twice as large as the other. Find the two angle measures.

Solution

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(From Unit 7, Lesson 2.)

Problem 5

Match each expression in the first list with an equivalent expression from the second list. 

A:

 \(7(x+2) - x + 3\)

B:

 \(6x + 3 + 4x + 5\)

C:

\(\frac {\text{-}2}{5}x - 7 + \frac35x - 3\)

D:

\(8x - 5 + 4 - 9\)

E:

\(24x + 36\)

1:

 \(\frac15x -10\)

2:

 \(6x+17\)

3:

 \(2(5x+4)\)

4:

 \(12(2x+3)\)

5:

\(8x +(\text-5) + 4 + (\text-9)\)

Solution

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(From Unit 6, Lesson 22.)

Problem 6

Clare paid 50% more for her notebook than Priya paid for hers. Priya paid \(x\) for her notebook and Clare paid \(y\) dollars for hers. Write an equation that represents the relationship between \(y\) and \(x\).

Solution

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(From Unit 4, Lesson 8.)