Question

If a cube of edge length 4 ft is cut from the corners a rectangular prism of length 6 ft, width 4 ft, and height 7 ft as shown, then what would be the total surface area of the resulting shape?

• A. $150$ sq ft
• B. $156$ sq ft
• C. $160$ sq ft
• D. $162$ sq ft

Answer 1

The correct option is B $156$ sq ft


Total surface area = Area of the bottom base + Area of the top base + Area of the L-shaped faces + Area of the back face + Area of the front faces

$=6\times 4+4\times 2+2\times [4\times 2+3\times 6]+7\times 4+[2\times 4\times 4+4\times 3]$
$=24+8+52+28+32+12$
$=156$ sq ft

The total surface area of the resulting shape is $156$ sq ft.