How do you find the volume of a cone in terms of pi when given the height and slant hight? height=16cm. slant height=20cm.

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lemjay's profile pic

lemjay | High School Teacher | (Level 3) Senior Educator

Posted on

Apply the formula of volume of cone which is:

`V=1/3pir^2h`

where r is radius of the base and h is height of the cone.

Since r is not given, use the Pythagorean formula to determine r. Note that the height (h), slant height (s) and the radius (r) forms a right triangle, wherein the s is the hypotenuse.

`s^2=r^2+h^2`

`20^2=r^2+16^2`

`400=r^2+256`

`400-256=r^2+256-256`

`144=r^2`

`+-sqrt144=sqrt(r^2)`

`+-12=r`

Since r represents the radius of the base of the cone, take only the positive value. Hence, r=12 cm.

Now that the value of r is known, plug-in h=16 and r=12 to the formula of volume of cone.

`V=1/3*pi*12^2*16`

`V=1/3*pi*144*16`

`V=768pi`

Hence, the volume of the given cone is  `768pi`  `cm^3` .

Jyotsana's profile pic

Jyotsana | Student, Grade 10 | (Level 1) Valedictorian

Posted on

a^2+b^2=c^2    b=radius

16^2+b^2=20^2

256+b^2=400

256+b^2-256=400-256

b^2=144

b=12

v=1/3*pi*r^2*h

v=1/3*pi*12^2*16

v=768pi

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