Question

How much liquid will fit in the glass shown? Round your answer to the nearest hundredth.

*** Must show all work/steps and explain your reasoning for credit!!

Answer 1

`91.63 in^3`

Explanation:

1. Ok, so first off let's break this down. There are two shapes shown in the glass if you look carefully. A cylinder and a hemisphere.

2. The volume formula of a cylinder is
`\pi r^2h` and the volume formula of a hemisphere is
`4/3\pi r^3` divided by 2.

3. Start off with the cylinder. You are given the height (3 in) and the diameter (5 in). You need the radius, which is half of the diameter so the radius would be 2.5

4. Plug in. You should have
`\pi (2.5)^2(3)` which gives you 58.90486225. Keep this number because it will be in use later.

5. The hemisphere. All you need is the radius, which we have (2.5) so plug in. You should have
`(4)/(3) \pi (2.5)^3` which gives you 65.44984695, now because this is a hemisphere you need to divide this number by 2 which gives you 32.72492348.

6. Now just add the volumes of the cylinder and the hemisphere together

7. You get 91.62978573.

8. Round to the nearest hundredth. You get your final answer of 91.63 in^3