Question

What is the surface area (in cm2) of a cuboid whose base is a square with perimeter 163 cm and whose height is 5 times its breadth?

Answer 1

If the perimeter of the base square is 163cm, then the length of the side is 163/4, since the perimeter of a square is 4a.

Thus, side of the square = 163/4 = 40.75.

Given that the height of the cuboid is 5 times breadth, the height of the cube is 40.75 * 5 = 203.75 cm.

Thus, the surface area of the cuboid is a*a + 4*a*h, since there are four rectangles and two base squares.

Therefore the surface area = 40.75*40.75 + 4*40.75*203.75

= 40.75*(40.75+4*203.75) = 40.75*(40.75+815) = 40.75*855.75 = 34871.8125 sq. cm.

Thus, the surface area is 34871.8125 sq. cm.