Question

Cones A and B Both have volume 48piπ cubic unit,but have different dimensions.Cone A has radius 6 units and height 4 units. Which answer can be the radius and height of Cone B?A.Radius=2and height = 12 B.Radius =4 and height=9C.Radius=3 and height=4D:Radius=4 and height=6

Answer 1

Option B is the only correct answer.

The possible dimensions of cone B is Radius = 4, Height = 9

Step-by-step explanation

The volume of a cone is given as

Volume of a cone = ⅓ (πr²h)

where

π = pi

r = radius of the cone

h = height of the cone

So, for each of these answer options, we will check the volume of the corresponding cone to see which one will give the volume of the cones in the question; 48π cubic units

Option A

Radius = 2 and height = 12

Volume of a cone = ⅓ (πr²h)

r = 2

h = 12

Volume of a cone = ⅓ (πr²h)

Volume of a cone = ⅓ (π) (2²) (12) = (48π/3) = 16π

This is not the answer because 16π ≠ 48π

Option B

Radius = 4 and height = 9

Volume of a cone = ⅓ (πr²h)

r = 4

h = 9

Volume of a cone = ⅓ (πr²h)

Volume of a cone = ⅓ (π) (4²) (9) = (144π/3) = 48π

This is an answer because 48π = 48π

Option C

Radius = 3 and height = 4

Volume of a cone = ⅓ (πr²h)

r = 3

h = 4

Volume of a cone = ⅓ (πr²h)

Volume of a cone = ⅓ (π) (3²) (4) = (36π/3) = 12π

This is not the answer because 12π ≠ 48π

Option D

Radius = 4 and height = 6

Volume of a cone = ⅓ (πr²h)

r = 4

h = 6

Volume of a cone = ⅓ (πr²h)

Volume of a cone = ⅓ (π) (4²) (6) = (96π/3) = 32π

This is not the answer because 32π ≠ 48π

Hope this Helps!!!