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.

Question

asked Sep 6, 2024 44.2k views

1 Answer

Zelocalhost · Answer 1 · 2024-09-12T08:30:32+0000

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 :

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 ;)