# What is the radius of the base of a cone whose volume is 63 cm^3 and height is 4 cm?

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We know that the volume of the cone is:

V = (1/3) * area of the base (a) * height (h)

63 = (1/3)*a* 4

63= 4/3) *a

==> a= 63*(3/4) = 47.25 cm^2

But we know that the area is:

a= pi*r^2 (where r is the radius and pi=3.14)

==> 47.25= (3.14)*r^2

==> r^2 = 47.25/3.14= 15.05 (approx.)

==> r= sqrt(15.05) = 3.88 cm (approx.)

The volume of a cone is given by the formula:

Volume = (1/3)*pi*(r^2)*h

Where:

r = Radius of the base of cone

h = height of cone

Substituting the given value of volume and r in the formula for volume:

63 = (1/3)*3.14159i*(r^2)*4

63 = 4.18879*r^2

Therefore:

r^2 = 63/4.18879

and:

r = (63/4.18879)^(1/2) = 3.8782

Answer:

Radius of base of the cone = 3.8782 cm

A cone with a height h and whose base has a radius r , has a volume V and is given by:

V = (1/3)pi*r^2*h........(1).

Here, r is to be determined and h = 4cm and V = 63 cm^3

From (1), making r subject:

r = sqrt{3V/(pi*r^2)} = {3*63/(pi*4)}^(1/2)

= 3.8782 cm