Question

Cones A and B both have volume cubic 48π units, but have different dimensions. Cone A has radius 6 units and height 4 units. Find one possible radius and height for Cone B. Explain how you know Cone B has the same volume as Cone A.

Answer 1

Answer:

r = 2 units

h= 36 units

Step-by-step explanation:

Given That:

Cones A and B both have volume cubic 48π units

The volume of a cone = $\frac{1}{3} \pi r^2h$

So for cone A

$V_A = \frac{1}{3} \pi r_A^2 h_A$

Volume for cone B

$V_B = \frac{1}{3} \pi r_B^2 h_B$

Due to different dimensions;

Cone A has

radius = 6 units

height = 4 units

To determine the one possible radius and height for cone B;

we have

$\frac{1}{3} \pi r_A^2 h_A =\frac{1}{3} \pi r_B^2 h_B$

$\frac{1}{3} \pi (6)^2 (4) =\frac{1}{3} \pi r_B^2 h_B$

$150.9=\frac{1}{3} \pi r_B^2 h_B$

$150.9=1.047r_B^2 h_B$

$r_B^2 h_B=144.12$

$r_B^2 h_B=144$

Therefore; the only possible way for this equation is :

$r_B = (2)\\h_B = 36$

If we are to check: we will realize that;

$r_B^2h_B = (2)^2*36 =144$

Therefore, the possible radius for the cone B = 2 units and height = 36 units. Hence from the question, we are told they both have the same volume of 48 π units.

Answer 2

Answer:

r= 4,

h= 9

Step-by-step explanation:

Since both Cones A and B share the same volume and we were told to derive any possible height and radius for cone B.

Therefore, using the formula for volume of a cone,we have; 1/3×pie×r2×h.

Multiply the radius and the height of cone A and it will give u the pathway to get the dimensions of B

So:6*6*4= 144(i.e for Cone A)

Find any number that will divide 144 and still have a figure which will have a perfect square root...

...9 is a good example. So 144/9 = 16 and the square root of 16= 4

So the radius of cone B is 4 and the height is 9.