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Spheres: Volume and Surface Area
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Spheres: Volume and Surface Area

lesson introduction

Spheres: Volume and Surface Area

Spheres require specific formulae to find their volumes and surface area.

As well as prisms, there are other special 3D shapes that have specific formulae. These include spheres, cones and pyramids.

1

This is the formula for the volume of a sphere

rr is the radius. We can use this for a sphere of any size.

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What is the volume of a sphere, of radius 9cm9cm, in terms of π\pi?

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1

This is the formula for the volume of a pyramid

A pyramid takes up 13\dfrac{1}{3} of the space compared to the cuboid which joins each of its vertices together. Notice that this is similar to the area, but there is an extra dimension involved.

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2

Similarly, this is the formula for the volume of a cone

Notice that this is essentially the same. πr2\pi r^2 is the area of the circular base and hh is the height, measured vertically from the base to the top of the pyramid. The 13\dfrac{1}{3} accounts for the thinning near the top.

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Given that a cone has a volume of 100πm3100 \pi m^3 and a height of 12m12m, what is its radius?

1

First, put the values you know into the formula

V=13πr2h100π=13π×r2×12V = \dfrac{1}{3} \pi r^2h \rightarrow 100\pi = \dfrac{1}{3} \pi \times r^2 \times 12

2

Simplify the equation

100π=13π×r2×12100π=4πr2100\pi = \dfrac{1}{3} \pi \times r^2 \times 12 \rightarrow 100\pi = 4\pi r^2

3

Rearrange the equation to make r2r^2 the subject

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4

If r2=25r^2=25, what is rr?

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