Find the volume $V$ of a pyramid if side $a = 4 cm$ and slant height $s = 5 cm$ .

Answer

$\frac{16 21}{3} cm^{3}$

Explanation

STEP 1: find height $h$

To find height $h$ use Pythagorean Theorem:

h^{2} + \frac{a ^{2}}{4} = s^{2}

After substituting $a = 4 cm$ and $s = 5 cm$ we have:

h^{2} + \frac{( 4 cm ) ^{2}}{4} = (5 cm)^{2}

h^{2} + \frac{16 cm ^{2}}{4} = (5 cm)^{2}

h^{2} + 4 cm^{2} = (5 cm)^{2}

h^{2} = 25 cm^{2} - 4 cm^{2}

h^{2} = 21 cm^{2}

h = 21 cm^{2}

h = 21 cm

STEP 2: find volume $V$

To find volume $V$ use formula:

V = \frac{a ^{2} \cdot h}{3}

After substituting $a = 4 cm$ and $h = 21 cm$ we have:

V = \frac{16 cm ^{2} \cdot 21 cm}{3}

V = \frac{16 21 cm ^{3}}{3}

V = \frac{16 21}{3} cm^{3}

This page was created using

Pyramid Calculator

About the Author

Welcome to MathPortal. This website's owner is mathematician Miloš Petrović. I designed this website and wrote all the calculators, lessons, and formulas.

If you want to contact me, probably have some questions, write me using the contact form or email me on mathhelp@mathportal.org.

Send Me A Comment

Main Navigation

Online Math Calculators

Find the volume V of a pyramid if side a=4cm and slant height s=5cm.

31621​​cm3

Find the volume $V$ of a pyramid if side $a = 4 cm$ and slant height $s = 5 cm$ .

$\frac{16 21}{3} cm^{3}$