Spheres

Lesson 3: Surface Area - Spheres

   Constructing Knowledge

Another type of three-dimensional object is a sphere.

Sphere An object whose surface points are all equidistant from its centre. This distance is called the radius.

The formula for the surface area of a sphere is written as:

\(\text{SA}_{\text{sphere}}=4\pi r^2\)

   Multimedia

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

EXAMPLE 1

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Determine the surface area of a sphere with a radius of 7.5 feet, to the nearest square foot.

Solution

Step 1: Draw and label a diagram.

• the radius is 7.5 feet

Step 2: Choose the appropriate surface area formula.

\(\text{SA}_{\text{sphere}}=4\pi r^2\)

Step 3: Calculate the surface area.

\(\begin{align} \text{SA}_{\text{sphere}}&=4\pi\left(7.5\,\text{ft}\right)^2 \\ \\ &=4\pi\times 56.25\,\text{ft}^2 \\ \\ &=707\,\text{ft}^2 \\ \end{align}\)

The surface area of a sphere with a radius of 7.5 ft is approximately 707 ft².




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