Lesson 3: Surface Area - Pyramid and Cones Examples

   Multimedia

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



EXAMPLE 1

These Vietnamese nón lá hats are now created in factories instead of by hand. What is the surface area of a hat with a diameter of 16 inches and a slant height of 10 inches? Round your answer to the nearest tenth of a square inch.

Solution


The hats don’t have a base, so the base will not be included in the surface area calculation. The surface area without the base is called the lateral surface area.

Step 1: Draw and label a diagram.



  • The diameter is 16 inches
  • The slant height is 10 inches
  • the radius needs to be calculated:

\(\begin{align} \text{radius}&=\frac{\text{diameter}}{2} \\ \\ &=\frac{16\,\text{in}}{2} \\ \\ &=8\,\text{in} \end{align}\)

Step 2: Choose the appropriate surface area formula.

\(\text{Lateral Surface Area}_{\text{cone}}=\pi rs\)

Step 3: Calculate the surface area.

\(\begin{align} \text{Lateral Surface Area}_{\text{cone}}&=\pi\times 8\,\text{in}\times 10\,\text{in} \\ \\ &=251.3\,\text{in}^2 \\ \end{align}\)

The nón lá hat’s surface area is approximately 251.3 in2.

EXAMPLE 2

In ancient times, the Great Pyramid of Giza was constructed. It has a slant height of 186.4 m and a square base of length of 230.4 m. Determine the surface area of the pyramid, to the nearest square metre.

Solution


Step 1: Draw and label a diagram.


  • length is 230.4 m
  • width is 230.4 m
  • slant height is 186.4 m

Step 2: Choose the appropriate surface area formula.

\(\text{SA}_{\text{square pyramid}}=lw+ls+ws\)

Step 3: Calculate the surface area.

\(\begin{align} \text{SA}_{\text{square pyramid}}&=\left(230.4\,\text{m}\times 230.4\,\text{m}\right)+\left(230.4\,\text{m}\times 186.4\,\text{m}\right)+\left(230.4\,\text{m}\times 186.4\,\text{m}\right) \\ \\ &=53\,084.16\,\text{m}^{2}+42\,946.56\,\text{m}^{2}+42\,946.56\,\text{m}^{2} \\ \\ &=138\,977\,\text{m}^2 \\ \end{align}\)

The surface area of the Giza Pyramid is approximately 138 977 m2.


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



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