A solid 3-dimensional circular object is a sphere. Its surface is defined as the collection of points that are all equidistant from a central point (centre of the sphere). Half of a sphere is called a hemisphere.

Unlike solids we have seen so far, we cannot unwrap a sphere to get a 2D net and calculate its area. But this didn't stop mathematicians finding a way! Archimedes investigated spheres relative to cylinders, and eventually determined the formula for the surface area of a sphere to be:

Surface Area of a Sphere

$A=4\pi r^2$A=4πr2

Just as with cylinders, we might be asked to work with hemispheres or other fractions of spheres.

Practice Questions

Question 1

Find the surface area of the sphere shown.

Round your answer to two decimal places.

Question 2

Consider the following hemisphere with a radius of $8$8. Find the total surface area.

A hemisphere is depicted. A circle drawn in dashed lines represents the area of the sphere that is not directly visible and to show that it is a three-dimensional figure. The radius of the sphere measuring $8$ units is represented by a vertical dashed line.

Round your answer to three decimal places.

Question 3

A ball has a surface area of $A=50.27$A=50.27 $mm$ ². What is its radius?

Round your answer to two decimal places.

Outcomes

MS11-4

performs calculations in relation to two-dimensional and three-dimensional figures

5.025 Surface area of spheres

Spheres