Question

The volume of a right cone is 21 pi units. If its circumference measures 6 pi units, find its height.

Answer 1

$\huge\sf\blue{Solution :-}$

Given,

Volume of cone = 21π cm³

& It's Circumference = 6π

Find Radius,

★ Circumference = πr²

=> 6π = πr

=> 6π/π = r

=> r = 6 cm

Now,

★Volume of cone = 1/3πr²h

$= > 21\pi = \frac{1}{3} \times 36\pi \times h \\ = > 21\pi = 12\pi \times h \\ = > \frac{21\pi}{12\pi} = h \\ = > \frac{7}{4} = h \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = > h \: = 1.75 \: cm$

★Hence, The value of height is 1.75 cm

Hope it helps youu....!!!

Answer 2

Through the volume of the cone we will calculate the height, so we find that:

h=1.75 cm

How to calculate the volume of the cone?

The volume of the cone is calculated by multiplying the area of the base and the height. Since the base is a circle, we use the formula for the area of a circle times the height of that cone.

Organizing the information given in the statement we have:

• Volume of cone = 21π cm³
• Circumference = 6π
• Radius = 6

knowing the formula of the volume is:

$V = 1/3\pi r^2h\\(21\pi )= 1/3 \pi (6)^2h\\h= 1.75$

See more about volume at brainly.com/question/1578538