A cone has a volume of 2560π cm cubed and a heigh of 30 cm.

a) Find the radius of the cone.

b) Find the slant height of the cone.

c) Find the LA of the cone.

r = 16 cm

g = 34 cm

LA = 1708.16 cm^2

Step-by-step explanation:

We have that for the cone, the formula is as follows:

v = pi / 3 * r ^ 2 * h

the first thing they ask is to calculate the radius, therefore we solve for r

r ^ 2 = 3 * v / (pi * h)

replacing the volume and height, it remains:

r ^ 2 = 3 * 2560 * pi / (pi * 30)

r ^ 2 = 3 * 2560/30 = 256

r = 16

Now, to calculate the slant height, that is to say g, we can calculate it knowing the height and the radius:

g ^ 2 = r ^ 2 + h ^ 2

g ^ 2 = 16 ^ 2 + 30 ^ 2

g ^ 2 = 1156

g = 34

The lateral area of the cone is given by the following equation:

LA = pi * r * g

replacing

LA = 3.14 * 16 * 34

LA = 1708.16 cm ^ 2

the lateral area is 1708.16 cm ^ 2