Question

A nut company is determining how to package their new type of party mix. The marketing department is experimenting with different-sized cans for the party mix

packaging. The designers use the equation r = v/h to determine the radius of the can for a certain height / and volume V. The company decides they want the can
to have a volume of 1792 cm³. Find the radius of the can if the height is 16 cm. Keep your answers in simplified radical form.
ha

Answer 1

The radius of the can is found using the formula for the volume of a cylinder (πr²h), resulting in the radius, in simplified radical form, being 4√(7) cm.

Step-by-step explanation:

To find the radius of the can when the height is 16 cm and the volume is 1792 cm³, we can use the formula for the volume of a cylinder, which is V = πr²h. We have been given V and h, so we can rearrange the formula to solve for r:

V = πr²h → r²

= V / (πh) → r

= √(V / (πh))

By plugging in the values for V and h:

r = √(1792 cm³ / (π * 16 cm))

= √(1792 / (3.14159 * 16)) cm

After calculating, we find:

r = √(35.5) cm

≈ √(112) cm

The radius of the can in simplified radical form is √(112) cm, which can be further simplified to 4√(7) cm.