Enrique says that the value of Vis a rational number for any positive, nonzero integer value of x. Select all of the values of x that could be used as counterexamples to show that Enrique's conjecture is false. 8.NS.1 x=1 x x=2 = x = 4 x = 5 X = 8 x=9 x=

9514 1404 393

  a) 252 cm³, 252 cm², 705.6 g

  b) 240 cm³, 252 cm², 672 g

Step-by-step explanation:

The volume of each figure can be computed as the product of the base area (the side facing the viewer) and the "height" of the prism (the distance between bases).

The surface area of the prism is the sum of the two base areas and the "lateral area" consisting of the product of the base perimeter and the "height" of the prism.

The mass will be the product of volume and density.

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ai) The base is a 3 cm by 8 cm rectangle together with a trapezoid with bases 3 cm and 6 cm, and height 7 - 3 = 4 cm.

  B = (3 cm)(8 cm) +(1/2)(3 cm +6 cm)(4 cm) = 24 cm² +18 cm² = 42 cm²

The "height" is 6 cm, so the volume is ...

  V = Bh = (42 cm²)(6 cm) = 252 cm³

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aii) The perimeter of the base is the sum of its side lengths. Clockwise from left, the lengths are ...

  (8 +3 +2 +5 +3 +7) cm = 28 cm

Then the lateral area is ...

  LA = Ph = (28 cm)(6 cm) = 168 cm²

Adding this to the areas of the two bases, we get the total surface area:

  A = LA +2B = (168 cm²) + 2(42 cm²) = 252 cm²

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aiii) The mass is the product of volume and density:

  M = ρV = (2.8 g/cm³)(252 cm³) = 705.6 g

bi) This trapezoidal prism has a base that has bases of 6 and 9 cm, and a height of 4 cm. The area of the base is ...

  B = (1/2)(b1 +b2)h = (1/2)(6 cm + 9cm)(4 cm) = 30 cm²

Then the volume is ...

  V = Bh = (30 cm²)(8 cm) = 240 cm³

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bii) The lateral area is the perimeter of the base times the height of the prism:

  LA = Ph = (4 +6 +5 +9 cm)(8 cm) = 192 cm²

The total area is this area plus that of the two bases:

  A = LA +2B = (192 cm²) +2(30 cm²) = 252 cm²

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biii) M = ρV = (2.8 g/cm³)(240 cm³) = 672 g