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 = [tex]\frac{1}{3} \pi r^2h[/tex]
So for cone A
[tex]V_A = \frac{1}{3} \pi r_A^2 h_A[/tex]
Volume for cone B
[tex]V_B = \frac{1}{3} \pi r_B^2 h_B[/tex]
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
[tex]\frac{1}{3} \pi r_A^2 h_A =\frac{1}{3} \pi r_B^2 h_B[/tex]
[tex]\frac{1}{3} \pi (6)^2 (4) =\frac{1}{3} \pi r_B^2 h_B[/tex]
[tex]150.9=\frac{1}{3} \pi r_B^2 h_B[/tex]
[tex]150.9=1.047r_B^2 h_B[/tex]
[tex]r_B^2 h_B=144.12[/tex]
[tex]r_B^2 h_B=144[/tex]
Therefore; the only possible way for this equation is :
[tex]r_B = (2)\\h_B = 36[/tex]
If we are to check: we will realize that;
[tex]r_B^2h_B = (2)^2*36 =144[/tex]
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:
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.
