Question

A rectangular pyramid with a height of 21 cm has a volume of 728 cm³. Calculate the length of its base if its breadth is 8 cm.​

Answer 1

Hello !

Answer:

`\Large \boxed{\sf length=13cm}`

Explanation:

The volume of a pyramid is given by
`\sf V_(pyramid)=(1)/(3) * B* h` where B is the area of the base and h is the height.

This is a rectangular pyramid. We have where
`\sf B=l* w` l is the length and w is the width (breadth).

So
`\sf V_(pyramid)=(1)/(3) * l* w* h`

Given :

• h = 21 cm
• w = 8 cm
• l = x

• 
  `\sf V_(pyramid)=728cm^3`

Let's replace h, w, l,
`\sf V_(pyramid)` with their values in the previous formula :

`\sf 728=(1)/(3) * x* 8 * 21\\728=56x`

Let's solve for x !

Divide both sides by 56 :

`\sf (56x)/(56) =(728)/(56)\\ \boxed{\sf x=13cm}`

Have a nice day ;)