Question

All edges of a square pyramid are 30 cm each.Find its volume.

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Answer 1

Answer:

Volume of square pyramid=(a^2)(h/3)

To find h,

As it is a equilateral triangle,

h=a√3/2

 = 30√3/2

= 15√3

Then,

Volume= (30^2)[(15√3)/3]

             =900*5√3

              = 4500√3 cm^2

Therefore,the volume of the pyramid is 4500√3cm^2

Answer 2

All edges of the square pyramid are equal to 30 cm each. So the lateral edges and base edges have the same length.

• $\sf{a=e=30\ cm}$

where $\sf{a}$ is the base edge and $\sf{e}$ is the lateral edge.

If $\sf{h}$ is the height of the square pyramid,

$\longrightarrow\sf{h=\sqrt{e^2-\left[\left(\dfrac{a}{2}\right)^2+\left(\dfrac{a}{2}\right)^2\right]}}$

$\longrightarrow\sf{h=\sqrt{e^2-\left[\dfrac{a^2}{4}+\dfrac{a^2}{4}\right]}}$

$\longrightarrow\sf{h=\sqrt{e^2-\dfrac{a^2}{2}}}$

Since $\sf{e=a,}$

$\longrightarrow\sf{h=\sqrt{a^2-\dfrac{a^2}{2}}}$

$\longrightarrow\sf{h=\dfrac{a}{\sqrt2}\quad\quad\dots(1)}$

Hence the volume of the square pyramid is,

$\longrightarrow\sf{V=\dfrac{1}{3}\,a^2h}$

From (1),

$\longrightarrow\sf{V=\dfrac{a^3}{3\sqrt2}}$

Taking $\sf{a=30,}$

$\longrightarrow\sf{V=\dfrac{30^3}{3\sqrt2}}$

$\longrightarrow\sf{V=\dfrac{9000}{\sqrt2}}$

$\longrightarrow\sf{\underline{\underline{V=4500\sqrt2\ cm^3}}}$

On taking $\sf{\sqrt2=1.414,}$

$\longrightarrow\sf{\underline{\underline{V=6363\ cm^3}}}$