Question #f7144

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Question #f7144

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Answer 1 · 2018-01-18T19:40:32

See below.

Explanation:

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a)

Volume of a prism is given by:

Area of base x height.

$(2 c - 2) (3 c - 4)$ $color(blue)((2c-2)(3c-4))$

b)

$(2 c - 2) (3 c - 4) = 6 c^{2} - 14 c + 8$ $(2c-2)(3c-4)=color(blue)(6c^2-14c+8)$

c)

$(2 (2) - 2) (3 (2) - 4) = 4$ $(2(2)-2)(3(2)-4)=color(blue)(4)$

$6 {(2)}^{2} - 14 (2) + 8 = 4$ $6(2)^2-14(2)+8=color(blue)(4)$

d)

The surface area is the sum of all the areas of the 6 faces of the prism. Sides opposite each other have the same area, so there are 3 pairs of areas;

From diagram these are:

$2 \times (2 c - 2) (3 c - 4) = 12 c^{2} - 28 c + 16$ $2xx(2c-2)(3c-4)=12c^2-28c+16$

$2 \times (2 c - 2) (c + 7) = 4 c^{2} + 24 c - 28$ $2xx(2c-2)(c+7)=4c^2+24c-28$

$2 \times (3 c - 4) (c + 7) = 6 c^{2} + 34 c - 56$ $2xx(3c-4)(c+7)=6c^2+34c-56$

We add these results together:

$88812 c^{2} - 28 c + 16$ $color(white)(888)12c^2-28c+16$

$88884 c^{2} + 24 c - 28$ $color(white)(8888)4c^2+24c-28$

$88886 c^{2} + 34 c - 56$ $color(white)(8888)6c^2+34c-56$

$= 8 22 c^{2} + 30 c - 68$ $=color(white)(8)color(blue)(22c^2+30c-68)$

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Question #f7144

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