Volume and surface area

Stack identical layers and you've got a prism. Each layer's volume is its base area, times a thickness. So for prisms and cylinders, $V =$ base area $\times$ height.

Solid	Volume
Box	$l w h$
Cylinder	$π r^{2} h$
Pyramid	$\frac{1}{3}$ base area $\times h$
Cone	$\frac{1}{3} π r^{2} h$
Sphere	$\frac{4}{3} π r^{3}$

Work through it

A cylinder with radius 3 and height 10.

Base area. $π (3)^{2} = 9 π$

Multiply by the height. $90 π$

A box $2 \times 3 \times 4$ . Find the surface area.

There are three pairs of faces. $2 \times 3, 2 \times 4, 3 \times 4$

Add each and double. $2 (6 + 8 + 12) = 52$

A cone and a cylinder with the same base and height. Compare.

It takes exactly three cones to fill the cylinder.cone $= \frac{1}{3}$ cylinder

Watch out for this

Using cm² for volume.

Volume is three lengths multiplied, so it's cm³. Area is two lengths, cm².

The short version
Volume is the area of the base times the height. Work out the base area first, and keep the units cubed. Cones and pyramids get a

\frac{1}{3}

Your turn

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