Question

Fran's filing cabinet is 6ft in height, 1 1/3 ft wide, and 3ft long. She plans to paint all sides except the bottom of the cabinet. I have to Find the area of the sides she intends to paint.

Answer 1

Area of the cabinet to be painted = 56 ft²

Explanation:

The cabinet is shown in the diagram. To find the surface area of the cabinet we will find the surface area of the rectangular cuboid.

Surface Area= 2 lb+ 2hb + 2lh

where l = length , b= breadth and h= height.

From the figure we see that the area of the bottom is given by length * breadth so deducting this from the total surface area of the cuboid gives the surface of the cabinet.

Area of the cabinet to be painted= lb+ 2hb + 2lh

Putting the values we get

Area of the cabinet to be painted = lb+ 2hb + 2lh

= 3* 1 1/3 + 2( 6 * 1 1/3) + 2( 3* 6)

= 3* 4/3 + 2( 6 * 4/3) + 2( 3* 6)

= 4+ 2(8) +2(18)

= 4+16+ 36

56 ft²

This is the outside area of the cabinet which is found front,back, top and two sides that need to be painted.