Question

Please answer with a detailed and long explanation

Answer 1

Cone B has a greater volume.

Explanation:

Cone B has the greatest volume.

The volume of a cone is calculated using the following formula:

`\boxed{\bold{\tt{Volume\: of\:cone = (1)/(3)\pi*r^2h}}}`

where:

• π is a mathematical constant approximately equal to 3.14
• r is the radius of the cone
• h is the height of the cone

For Cone A.

`\boxed{\bold{\tt{Volume\: of\:cone\: (A)= (1)/(3)\pi*r^2h}}}`

For Cone B

In this case, the radius of Cone B is double the radius of Cone A, and the height of Cone B is half the height of Cone A. This means:

radius(r)=2r

height(h)=
`\tt{(1)/(2)*(h)/(2)}`

`\boxed{\bold{\tt{Volume\: of\:cone\: (B)= (1)/(3)\pi*(2r)^2*(h)/(2)}}}`

`\boxed{\bold{\tt{Volume \: of\:cone (B)= 2*(1)/(3)\pi*r^2h}}}`

`\boxed{\bold{\tt{Volume(B) =2*Volume\: of\:cone(A)}}}`

Since the volume of cone B is twice the volume of Cone A.

Therefore, Cone B has a greater volume.

Answer 2

The volume of Cone B is twice the volume of Cone A.

Explanation:

The volume of a cone is given by

V = 1/3 pi r^2 h where r is the radius and h is the height.

Cone A

d = diameter

r = radius

h = height

V = 1/3 pi r^2 h

Cone B

The diameter is double the diameter of A.

2d so the radius is 2r

The height is half the height of A.

1/2 h

Substitute into the equation for volume.

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

V = 1/3 pi (4r^2) (1/2h)

V = 1/3 pi 2r^2 h

The volume of Cone B is twice the volume of Cone A.