Identify the volume of a cone with a base area 25π m^2 and a height equal to three times the radius.

V = 392.7 m3

Step-by-step explanation:

To find the volume of the cone, first calculate the hieght and the radius.

To find the length of the radius, equate the given area to the formula for the area of a circle and solve for r.

πr2=25π

Divide both sides by π.

r2=25

Take the positive square root of both sides.

r=5 m

It is given that the height of the cone equal to three times the radius. So, use the radius to find the height.

h=3r

Substitute 5 for r.

h=3⋅5

Simplify.

h=15 m

To find the volume of the cone, use the formula for the volume of a cone.

V=13πr2h

Substitute 5 for r and 15 for h.

V=13⋅π⋅52⋅15

Simplify.

V=125π

Use a calculator to approximate.

V≈392.7 m3

Therefore, the volume of the cone is about 392.7 m3.