Identify the volume of a cone with base area 64π m2 and a height 4 m less than 3 times the radius, rounded to the nearest tenth.
a: v = 1280 m3
b: v = 4021.2 m3
c: v = 1340.4 m3
d: v = 670.2 m3

Correct V = 1340.4 m3

Step-by-step explanation:

To find the volume of the cone, first calculate the height 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=64π

Divide both sides by π.

r2=64

Take the positive square root of both sides.

r=8 m

It is given that the height of the cone 4 m less than 3 times the radius. So, use the radius to find the height.

h=3r−4

Substitute 8 for r and simplify.

h=3⋅8−4=20 m

To find the volume of the cone, use the formula for the volume of a cone, V=13πr2h.

Substitute 8 for r and 20 for h, then simplify.

V=13⋅π⋅82⋅20=12803π m3

Use a calculator to approximate.

V≈1340.4 m3

Therefore, the volume of the cone is about 1340.4 m3.