Question

Question #f7144

Answer 1

See below.

Explanation:

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)`