Find the volume $V$ of a cone if diameter $d = 27.056 cm$ and slant height $l = 25 cm$ .

Answer

$1993.0947 π cm^{3}$

Explanation

STEP 1: find radius $r$

To find radius $r$ use formula:

d = 2 \cdot r

After substituting $d = 27.056 cm$ we have:

27.056 cm = 2 \cdot r

r = \frac{27.056 cm}{2}

r = 13.528 cm

STEP 2: find side $h$

To find side $h$ use Pythagorean Theorem:

r^{2} + h^{2} = l^{2}

After substituting $r = 13.528 cm$ and $l = 25 cm$ we have:

(13.528 cm)^{2} + h^{2} = (25 cm)^{2}

h^{2} = (25 cm)^{2} - (13.528 cm)^{2}

h^{2} = 625 cm^{2} - 183.0068 cm^{2}

h^{2} = 441.9932 cm^{2}

h = 441.9932 cm^{2}

h = 21.0236 cm

STEP 3: find volume $V$

To find volume $V$ use formula:

V = \frac{h ^{2} \cdot r \cdot π}{3}

After substituting $r = 13.528 cm$ and $h = 21.0236 cm$ we have:

V = \frac{441.9932 cm ^{2} \cdot 13.528 cm \cdot π}{3}

V = \frac{5979.2842 cm ^{3} π}{3}

V = 1993.0947 π cm^{3}

This page was created using

Cone 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 cone if diameter d=27.056cm and slant height l=25cm.

1993.0947πcm3

Find the volume $V$ of a cone if diameter $d = 27.056 cm$ and slant height $l = 25 cm$ .

$1993.0947 π cm^{3}$