Question #f7144

1 Answer
Jan 18, 2018

See below.

Explanation:

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a)

Volume of a prism is given by:

Area of base x height.

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

b)

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

c)

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

2xx(2c-2)(3c-4)=12c^2-28c+16

2xx(2c-2)(c+7)=4c^2+24c-28

2xx(3c-4)(c+7)=6c^2+34c-56

We add these results together:

color(white)(888)12c^2-28c+16

color(white)(8888)4c^2+24c-28

color(white)(8888)6c^2+34c-56

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