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Volume

Volume of Pyramids

The volume of a pyramid is given by:

 Volume = $\frac{1}{3}$Area of base x Height V=$\frac{1}{3}$AH where A is the area of the base of the pyramid and H is the height.

The rule for finding the volume of a pyramid is the same no matter what polygon forms the base. Of course, how you find the area of the base will depend on the polygon that forms the base.

Find the volume of the square pyramid:

 V=$\frac{1}{3}$BH B = 302 = 900 cm2 Using Pythagorean Pythagorean: H2 = 172 - 152 = 289 - 225 = 64 H = 8 cm Therefore: V = $\frac{1}{3}$·900·8 = 2400 cm3

V=48$\sqrt{3}$ cm3
H=8cm
Find s

 V=$\frac{1}{3}$BH 48$\sqrt{3}$ =$\frac{1}{3}$ B · 8 3·6·$\sqrt{3}$=$\frac{1}{3}$ B·3 18$\sqrt{3}$ = B Let's look at the base: $A=(\frac{bh}{2})$ $18\sqrt{3}=(\frac{s\;\cdot\;\frac{\sqrt{3}s}{2}}{2})$ $18\sqrt{3}=(\frac{s^{2}\;\sqrt{3}}{4})$ 72$\sqrt{3}$ = s2$\sqrt{3}$ 72 = s2 s = $\sqrt{72}$ = $\sqrt{4}$$\sqrt{9}$$\sqrt{2}$ s = 6$\sqrt{2}$