Wize High School Grade 9 Math Textbook > 3D Geometry - Measurements

Surface Area & Volume of a Sphere

Surface Area of a Sphere

A sphere is a solid 3D object where every point on its surface is the same distance from the center.

Surface Area

The surface area of a sphere is 4 times the area of the circular cross-section through the middle of the sphere (passing through the diameter)

$\large\boxed{\text{S.A.}_\text{sphere}=4\pi r^2}$

Practice: Surface Area of a Sphere

Find the surface area of this sphere.

Enter the EXACT surface area of the sphere in $ft^2$, do not include units, do not round your answer.

I don't know

Volume of a Sphere

The volume of a sphere is $\dfrac{2}{3}$ the volume of the cylinder with the same circular base and the same height.

$\begin{array}{rcl} V&=&\dfrac{2}{3}\pi~ (r_\text{cylinder})^2\times h_\text{cylinder}\\ \end{array}$

From the diagram, we see that the radius of the cylinder is the radius of the sphere, and the height of the cylinder is 2 times the radius of the sphere:

$\begin{array}{rcl} V&=&\dfrac{2}{3}\pi~r^2\times (2r)\\ \end{array}$

Simplifying, we get the formula for the volume of a sphere with radius $r$ :

$\large\boxed{V_\text{sphere}=\dfrac{4}{3}\pi r^3}$

Practice: Volume of a Sphere

Find the volume of this sphere.

Enter the EXACT volume of the sphere in $ft^3$, do not include units, do not round your answer.

I don't know

Practice: Sphere

The outside of a soccer ball is made up of leather that costs $0.01/ $cm^2$ . If the volume of a spherical soccer ball is $5575~cm^3$ , what is the cost of leather needed to make this soccer ball?

Enter the cost of leather in $ rounded to 2 decimal places, do not include units.

I don't know

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Practice: Spheres

If the surface area and volume of a sphere are the same, what do we know about the radius of the sphere?

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Surface Area & Volume of a Sphere

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Surface Area of a Sphere

Surface Area

Practice: Surface Area of a Sphere

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Volume of a Sphere

Practice: Volume of a Sphere

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Practice: Sphere

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Practice: Spheres

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