Question

Noah and Lin are making paper cones to hold popcorn to hand out at parent math night. They want the cones to hold 9 cubic inches of popcorn. What are two different possible values for height h and radius r for the cones?
height (h)=

radius (r)=

Answer 1

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 = $\frac{1}{3}\pi r^{2}h$

As given,

V = $9\pi$

⇒$\frac{1}{3}\pi r^{2}h = 9\pi \\ \frac{1}{3} r^{2}h = 9 \\r^{2}h = 27$

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