Question

75 POINTS

A right cylinder has a radius of 5 cm and a height of 3 cm.

Answer the following questions and make sure to show all your work.

(a) Find the Volume of the cylinder.

(b) If you wanted more volume in your cylinder, which of these two ideas would give the most Volume?

1. Doubling the radius to 10 cm, while the height remains 3 cm.
-OR-
2. Tripling the height to 9 cm, while the radius remains 5 cm.

Answer 1

a) 235.62 cm³ (nearest hundredth)

b) 2. tripling the height to 9 cm, while the radius remains 5 cm, gives the most volume

Explanation:

volume of a cylinder =
`2\pi r^2h` (where r is the radius and h is the height)

Given:

• r = 5 cm
• h = 3 cm

a) ⇒ volume =
`\pi * 5^2 * 3=75\pi =235.62` cm³ (nearest hundredth)

b) Given:

• r = 10 cm
• h = 3 cm

⇒ volume =
`\pi * 10^2 * 3=300\pi =942.48` cm³ (nearest hundredth)

Given:

• r = 5 cm
• h = 9 cm

⇒ volume =
`\pi * 5^2 * 9=225\pi =706.86` cm³ (nearest hundredth)

Therefore, 2) tripling the height to 9 cm, while the radius remains 5 cm, gives the most volume