Answer :
Answer:
So, The possible values of h and r are
1. r = 3 , h = 3
2. r = 1, h = 27
3. r = 2, h = 6.75
Step-by-step explanation:
P.S - The exact ques is -
As we know that Volume of cone , V = [tex]\frac{1}{3}\pi r^{2}h[/tex]
As given,
V = [tex]9\pi[/tex]
⇒[tex]\frac{1}{3}\pi r^{2}h = 9\pi \\ \frac{1}{3} r^{2}h = 9 \\r^{2}h = 27[/tex]
So,
The possible values of h and r are
1. r = 3 , h = 3
2. r = 1, h = 27
3. r = 2, h = 6.75
In Case I-
When r = 3, h = 3
(3)² ×3 = 9×3 = 27
Satisfied
Case II-
r = 1, h = 27
(1)²×27 = 1×27 = 27
Satisfied
Case III-
r = 2, h = 6.75
(2)²×6.75 = 4×6.75 = 27
Satisfied
If the radius of the base of the cone is 2 inches then the height of the cone should be 2.1485 inches.
What is the volume of the cone?
The volume of the cone is the volume occupied by the cone. It is given by the formula,
[tex]\text{Volume of the cone}= \dfrac{1}{3} \pi r^2h[/tex]
where r is the radius of the base, and h is the height of the cone.
Now, as it is given that cones need to hold 9 cubic inches of popcorn. therefore, the volume of the cone can be written as,
[tex]\text{Volume of the cone}= \dfrac{1}{3} \pi r^2h\\\\9 \times 3 = \pi r^2h\\\\\dfrac{9 \times 3}{\pi}=r^2 h\\\\8.5943 = r^2 h[/tex]
Thus, the product of the square of the radius and the height of the cone should be such that the result is 8.5943.
Now, let the radius of the cone be 2 inches, therefore, the height of the cone is,
[tex]8.5943 = r^2 h\\\\8.5943 = (2^2) h\\\\h = 2.1485\rm\ in[/tex]
Hence, if the radius of the base of the cone is 2 inches then the height of the cone should be 2.1485 inches.
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