Another common type of solid is the **sphere**. Recall that a sphere is a solid consisting of all points at a fixed distance from a central point.

Unlike the solids we have seen so far, we cannot unwrap a sphere to get a 2D net to calculate its area, so the **surface area** of a sphere is approached in a different way.

So can calculate the surface area of a sphere using the formula:

\displaystyle SA = 4\pi r^{2}

\bm{r}

the radius of the sphere

We can calculate the volume of a sphere using the formula:

\displaystyle V = \dfrac{4}{3} \pi r^{3}

\bm{r}

the radius of the sphere

Find the surface area of a sphere with radius 3 \text{ cm}.

Worked Solution

The ice cream cones at an ice creamery have the dimensions indicated in the diagram:

a

Given that 1 cubic centimeter is equivalent to 1 milliliter, how many milliliters of ice cream can fit in each cone, including the hemisphere scoop on top? Round your answer to the nearest milliliter.

Worked Solution

b

The ice cream is bought in 10 \text{ L} tubs. How many whole cones can be made with a single tub of ice cream?

Worked Solution

c

Double cones are served with a second hemispherical scoop of the same dimensions as the first scoop. How many double cones can be made with from a 10 \text{ L} tub?

Worked Solution

A sphere has a radius that is r\text{ cm} long and a volume of \dfrac{512\pi}{3}\text{ cm}^{3}.

Find the radius of the sphere. Round your answer to two decimal places.

Worked Solution

A spherical lamp base, initially designed with a diameter of 10 inches, needs to be resized to fit a new space. Its diameter needs to be reduced by 20 percent.

a

What is the diameter of the lamp's base after the redesign?

Worked Solution

b

By what percentage does the surface area decrease due to the design change?

Worked Solution

c

By what percentage does the volume decrease due to the design change?

Worked Solution

Soledad has two spheres. The volume of the larger sphere is 4 times the volume of the smaller sphere. How much greater is the radius of the larger sphere than the smaller sphere?

Worked Solution

Idea summary

We can calculate the volume of a sphere using the formula:

\displaystyle V = \dfrac{4}{3} \pi r^{3}

\bm{r}

the radius of the sphere

We can calculate the surface area of a sphere using the formula:

\displaystyle SA = 4\pi r^{2}

\bm{r}

the radius of the sphere