Question

The height of a cone is two times its base diameter. What is the volume of the cone in terms of its base radius r?

A.V=
`(2)/(3)\\`(pi)(r²)
B.V=
`(4)/(3)\\`(pi)(r³)
C.V=
`(1)/(3)\\`(pi)(r³)
D.V=
`(1)/(3)\\`(pi)(r²)

Answer 1

Answer: B

h=2d

r=d/2

so h in terms of r is;

h=4r

V=pi*r^2*h/3

V=pi*r^2*4r/3=pi*4r^3/3=4/3(pi)(r^3)

Answer 2

B

Explanation:

Assume the radius is r so the diameter is 2r

Height=2*d=2(2r)=4r since the diameter is twice the radius

Volume of cone=1/3 * pi*r^2*h

= 1/3 * pi*r^2*(4r)

=4/3 *pi *r^3

So B