Lesson 3: Surface Area - Right Prisms and Right Cylinders Examples

   Constructing Knowledge

To calculate the surface area of objects, follow these steps.

Step 1: Draw and label a diagram.

Step 2: Choose the appropriate surface area formula and substitute the known values into the formula.

Step 3: Calculate the surface area.

   Multimedia

A video demonstration of calculating the surface area of a cylinder is provided.



EXAMPLE 1

A right cylinder is given with a radius of 2.5 cm and a height of 7.5 cm. Determine the surface area of the cylinder, to the nearest tenth of a square centimetre.

Solution


Step 1: Draw and label a diagram.



  • the radius is 2.5 cm
  • the height is 7.5 cm

Step 2: Choose the appropriate surface area formula.

\(\text{SA}_{\text{cylinder}}=2\pi r^{2}+2\pi rh\)

Step 3: Calculate the surface area.

\(\begin{align} \text{SA}_{\text{cylinder}}&=2\pi\left(2.5\,\text{cm}\right)^{2}+2\pi\left(2.5\,\text{cm}\right)\left(7.5\,\text{cm}\right) \\ \\ &=39.269\,\text{cm}^{2}+117.809\,\text{cm}^2 \\ \\ &=157.1\,\text{cm}^2 \\ \end{align}\)

The surface area of the right cylinder is 157.1 cm2.

EXAMPLE 2

The right equilateral triangular prism shown has a height of 15 cm. The triangular base has a height of 3.5 cm and side lengths of 4 cm.

Solution


Step 1: Draw and label a diagram.

Sometimes a net is an easier type of diagram to work with.



  • length of rectangle is 15 cm
  • width of rectangle is 4 cm
  • base of triangle is 4 cm
  • height of triangle is 3.5 cm

Step 2: Choose the appropriate surface area formula.

\(\text{SA}_{\text{triangular prism}}=lw+lb+lh+bh\)

Step 3: Calculate the surface area.

\(\begin{align} \text{SA}_{\text{triangular prism}}&=\left(15\,\text{cm}\times 4\,\text{cm}\right)+\left(15\,\text{cm}\times 4\,\text{cm}\right)+\left(15\,\text{cm}\times 4\,\text{cm}\right)+\left(4\,\text{cm}\times 3.5\,\text{cm}\right) \\ \\ &=60\,\text{cm}^{2}+60\,\text{cm}^{2}+60\,\text{cm}^{2}+14\,\text{cm}^{2} \\ \\ &=194\,\text{cm}^2 \\ \end{align}\)

The surface area of the prism is 194 cm2.


Now, it is your turn! Complete the questions in your Chapter 7, Lesson 3 Practice Makes Perfect that refer to Right Prisms and Right Cylinders.



2014 © Alberta Distance Learning Centre