Functional Skills: Surface Area

Example: Calculate the surface area of the cuboid.

The area of the front face and back face are both $textcolor{blue}{8} times textcolor{blue}{3} = 24 text{ cm}^2$

The area of the side faces are both $textcolor{blue}{5} times textcolor{blue}{3} = 15text{ cm}^2$

The area of the top face and bottom face are both $textcolor{blue}{8} times textcolor{blue}{5} = 40text{ cm}^2$

Therefore, the total surface area is

$(2 times 24) + (2 times 15) + (2 times 40) = 48 + 30 + 80 = 158 text{ cm}^2$

Example: Calculate the surface area of the cylinder.

Give your answer to the nearest whole number.

Use $pi = 3.14$

You can draw the net of this cylinder to help:

The net has two circles of radius $textcolor{red}{4}$ cm, and a rectangle of width $textcolor{blue}{5}$ cm and length which is equal to the circumference of the circles.

First, calculate the circumference of the circle:

circumference $= pi d = 2 pi r = 2 times 3.14 times textcolor{red}{4} = 25.12$ cm

Then, calculate the areas of the faces:

area of rectangle $= 25.12 times textcolor{blue}{5} = 125.6$ cm$^2$

area of circle $=pi r^2 = 3.14 times textcolor{red}{4}^2 = 50.24$ cm$^2$